VRIJE UNIVERSITEIT BRUSSEL Acoustics - the Dept. of ...

VRIJE UNIVERSITEITBRUSSELAcousticsBruface Master 1 Electromechanical EngineeringProf. S. Vanlanduit

PrefaceSound is caused by the vibration of air particles. Sound can also be representedas a wave, propagating in a certain media (air, steel, et cetera... ).Soundisaperfectmeansofcommunication. Spokenlanguageisanecessity inour contemporary society. It is difficult to imagine our world without sound.A total absence of sound (like in an anechoic room) feels weird although itcould be a blessing sometimes. Sound has many pleasurable aspects: listeningto your favourite music, a phone call from your friend, an aria of LucianoPavarotti, the growling of the engine of a sports car. It is clear that thenotion of a sound being pleasurable or not is subjective. The sounds emittedduring an activity will in most cases not hinder the executor. This samesound however, can hinder a person in the proximity. The interpretation ofsound is highly individual, meaning that it is a factor that is hard to takeinto account. For example; listening to modern music, played extremely loudcan be a lust for daughter or son; whereas it causes annoyance for father andmother. The lawnmower of your neighbour can irritate you while the soundof your own one doesn’t bother you. There is a thin line between sound andsound pollution. In other cases (like noise pollution on the shop floor) itis quite obvious. One could think of a distinction between sound and noisepollution on basis of the sound level. This is the way the difference is definedin current legislation. It is clear however that not only the sound level determinesif we are dealing with sound pollution. The time of day, the activityof a person and his/her mood play a role as well. A leaking tap can cause alarge irritation during the night, and no irritation at all during the day.i

iiWhen sound becomes noise, it will hinder us and start to annoy. At thispoint we call it sound pollution (or noise pollution). Sound pollution notonly occurs on the shop floor but in our daily lives as well. There existmultiple causes of sound pollution: industry, traffic, trains, airplanes, disco’set cetera. Noise is sound that:causes hinder, disturbs or is uncomfortablecauses harmor has both consequencesNoise must always be contested because it poses some risks for man.The most notable being hearing impairment. When someone is exposed tocertain noises for a to long period of time, their hearing capabilities will degrade.In some cases it is only temporary; after some rest the hearing willrecover. In other cases irreversible damage is caused, because no or insufficientprecautions were taken to reduce the noise or to protect the hearing.The occupational hearing impairment or deafness is included on the list ofoccupational disabilities. Noise or unwanted sounds can lead to: stomachulcers; high blood pressure; headache; infection of the large intestine; raisedpulsation; dilatation of the eye pupil; palpitations; reaction of the Skeletalstriated muscle; vasoconstriction. Noise has an indirect negative influence onthe general health, because it causes feelings of hinder, anger, tension, andanxiety. Noise is probably a far greater risk for the general health than wasassumed in the past.One could think that noise pollution only occurs in our time. This is nottrue however, as is indicated in the following chronicle: At the time of thereign of Queen Elisabeth II (1533 - 1603) a law was enforced that forbademale nationals from beating their wives after 10 pm. The screaming of thevictims was said to disrupt the good nights sleep of the neighbours. Evenother writings (incl. Horatius, 65-8 BC) complained about the increasingnoise in the cities. It is clear for everyone that sound pollution increasesdaily due to the ever increasing contribution of traffic, industry, and hobbies.In the following modules we will discuss how we can deal with this problempractically and scientifically sound.The permissible noise level for different application areas is regulatedextensively in legislation. In this course we will focus on three recent Europeandirectives regulating the noise pollution in the environment and on theworkfloor. The main objectives and actions of these European directives aredescribed in Part III of the course.In each of these directives the primary objective is to limit the noise a thelevel of the sound source as much as possible. In Chapter 6 some practical

measures that can be used to reduce the sound production in an industrialenvironment are outlined. In practice, it is not always possible to modifythe sound source itself because of financial implications. In that case onecan consider reducing the transfer of sound to the receiver. In Chapter 5the transmission of sound through a wall is studied. A simple calculationmethod is introduced to calculate the transmission loss based on materialproperties of the wall. This so called mass-frequency law formula then allowsone to calculate the required thickness of an enclosure to reduce the noiselevel to acceptable level. In order to significantly reduce the noise level ofa source, acoustic absorption should also be applied in addition to soundinsulation. The latter means that the walls of an enclosure are treated toeliminate reflections at the wall possibly leading to an amplification of thesound (giving rise to an acoustic resonance). This is described in Chapter 4.Before the elements of noise control are outlined, the fundamental conceptsof acoustics are given in Chapter 1.iii

ContentsI Introduction to acoustics 11 Fundamental Concepts of Acoustics 31.1 Definition and origin of sound . . . . . . . . . . . . . . . . . . 31.2 Plane sound waves . . . . . . . . . . . . . . . . . . . . . . . . 41.2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 The speed of sound . . . . . . . . . . . . . . . . . . . . 61.2.3 The one-dimensional wave equation . . . . . . . . . . . 81.2.4 Acoustic impedance of a medium . . . . . . . . . . . . 111.3 Spherical sound waves . . . . . . . . . . . . . . . . . . . . . . 111.4 Cylindrical sound waves . . . . . . . . . . . . . . . . . . . . . 121.5 Sound levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.5.1 The effective sound pressure . . . . . . . . . . . . . . . 131.5.2 The dB-scale . . . . . . . . . . . . . . . . . . . . . . . 141.5.3 Superposition of two sounds . . . . . . . . . . . . . . . 161.5.4 Types of sound . . . . . . . . . . . . . . . . . . . . . . 181.6 The acoustic intensity . . . . . . . . . . . . . . . . . . . . . . 181.6.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . 181.6.2 The sound intensity level . . . . . . . . . . . . . . . . . 201.7 Source power . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.7.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . 201.7.2 The sound field produced by a point source . . . . . . 212 The human hearing system 232.1 Anatomy of the ear . . . . . . . . . . . . . . . . . . . . . . . . 232.1.1 The external ear . . . . . . . . . . . . . . . . . . . . . 232.1.2 The middle ear . . . . . . . . . . . . . . . . . . . . . . 232.1.3 The internal ear . . . . . . . . . . . . . . . . . . . . . . 242.2 Physiology of the ear . . . . . . . . . . . . . . . . . . . . . . . 252.2.1 The auditory field . . . . . . . . . . . . . . . . . . . . . 252.2.2 Amplification of signals in hearing . . . . . . . . . . . . 262.3 Pathology of the ear . . . . . . . . . . . . . . . . . . . . . . . 30v

viCONTENTS2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 302.3.2 Development of the ear with age . . . . . . . . . . . . . 302.4 The human perception of sound . . . . . . . . . . . . . . . . . 312.4.1 The phon . . . . . . . . . . . . . . . . . . . . . . . . . 312.4.2 The sone as measure of loudness . . . . . . . . . . . . . 313 Measuring sound 333.1 Introduction: why measure sound . . . . . . . . . . . . . . . . 333.2 The measurement microphone . . . . . . . . . . . . . . . . . . 333.2.1 Size of the microphone . . . . . . . . . . . . . . . . . . 353.2.2 The sound field where measurements take place . . . . 363.2.3 Influence of the wind speed . . . . . . . . . . . . . . . 373.2.4 Division of sound in frequency bands . . . . . . . . . . 393.3 Frequency weighting of microphone signals . . . . . . . . . . . 413.4 The sonometer . . . . . . . . . . . . . . . . . . . . . . . . . . 423.5 Calibration of measurement systems . . . . . . . . . . . . . . . 443.6 Presence of the observer . . . . . . . . . . . . . . . . . . . . . 443.7 Background noise . . . . . . . . . . . . . . . . . . . . . . . . . 453.8 Quantitative parameters . . . . . . . . . . . . . . . . . . . . . 463.8.1 The equivalent sound pressure level . . . . . . . . . . . 463.8.2 Sound Exposure Level . . . . . . . . . . . . . . . . . . 473.8.3 Statistic sound levels . . . . . . . . . . . . . . . . . . . 473.8.4 The Noise Rating value . . . . . . . . . . . . . . . . . . 483.8.5 The nuisance of fluctuating sound . . . . . . . . . . . . 493.9 The intensity meter . . . . . . . . . . . . . . . . . . . . . . . . 503.10 Measuring sound sources . . . . . . . . . . . . . . . . . . . . . 523.10.1 Measurements in an anechoic half-space . . . . . . . . 523.10.2 Measurements in a full anechoic room . . . . . . . . . . 543.10.3 The comparison method . . . . . . . . . . . . . . . . . 553.10.4 Power measurement with an intensity meter . . . . . . 55II Noise control 574 Sound Absorption 594.1 Acoustic transmission between two media . . . . . . . . . . . . 594.1.1 Normal incidence . . . . . . . . . . . . . . . . . . . . . 604.2 Realization of acoustic absorption . . . . . . . . . . . . . . . . 644.2.1 Plate on an air layer . . . . . . . . . . . . . . . . . . . 644.2.2 Helmholtz resonator . . . . . . . . . . . . . . . . . . . 654.2.3 Porous acoustic absorbing materials . . . . . . . . . . . 67

CONTENTSvii4.3 Measuring the acoustic absorption . . . . . . . . . . . . . . . . 704.3.1 Reverberation time . . . . . . . . . . . . . . . . . . . . 704.3.2 Measuring the absorption in a reverberation room . . . 754.3.3 Measuring the absorption in the Kundt tube . . . . . . 754.4 The direct and diffuse sound field . . . . . . . . . . . . . . . . 775 Sound Insulation 815.1 Measuring sound insulation . . . . . . . . . . . . . . . . . . . 815.1.1 Measuring airborne sound insulation . . . . . . . . . . 815.1.2 Measurement of impact sound . . . . . . . . . . . . . . 845.1.3 Single number rating . . . . . . . . . . . . . . . . . . . 855.2 Airborne sound insulation of a wall . . . . . . . . . . . . . . . 865.2.1 Simple law . . . . . . . . . . . . . . . . . . . . . . . . . 865.2.2 Effect of the wall stiffness . . . . . . . . . . . . . . . . 885.2.3 The coincidence effect . . . . . . . . . . . . . . . . . . 905.2.4 Insulation of double wall constructions . . . . . . . . . 925.2.5 Insulation of a composite wall . . . . . . . . . . . . . . 945.3 The acoustical barrier . . . . . . . . . . . . . . . . . . . . . . 956 Noise control 996.1 Origin of noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 996.2 Reducing noise at the level of the sound source . . . . . . . . . 1026.2.1 Aerodynamic noise sources . . . . . . . . . . . . . . . . 1026.2.2 Sources of hydrodynamic noise . . . . . . . . . . . . . . 1056.2.3 Sources of structure-borne noise . . . . . . . . . . . . . 1086.3 Tackling noise transmission . . . . . . . . . . . . . . . . . . . 1106.3.1 Transmission of aerodynamic noise . . . . . . . . . . . 1106.3.2 Hydrodynamic noise transmission . . . . . . . . . . . . 1126.3.3 Structure-borne noise transmission . . . . . . . . . . . 1136.4 Radiation noise . . . . . . . . . . . . . . . . . . . . . . . . . . 115III Noise directives 1197 Directive 2000/14/EG : ’Machines in open air’ 1238 Noise on the work floor 1278.1 Previous guideline . . . . . . . . . . . . . . . . . . . . . . . . . 1278.2 Present guideline: directive 2003/10/EG . . . . . . . . . . . . 1298.3 Risk of hearing damage . . . . . . . . . . . . . . . . . . . . . . 1328.4 The audiometric examination . . . . . . . . . . . . . . . . . . 135

viiiCONTENTS8.4.1 Personal hearing protection . . . . . . . . . . . . . . . 1379 Community noise 1399.1 EC directive 2002/49/EC . . . . . . . . . . . . . . . . . . . . 139A Material properties 143

Part IIntroduction to acoustics1

Chapter 1Fundamental Concepts ofAcoustics1.1 Definition and origin of soundWhen an external mechanical excitation is applied on a material, a liquid ora gas, vibrations are induced in it. The molecules of the medium vibratesaround an equilibrium position. If this phenomenon occurs in a solid or aliquid, we talk about vibrations. The term sound is used if air is the medium,as long as it can be perceived by the human ear. This latter concept can beexplained by means of a simple example (Figure 1.1): a tuning fork is struckand produces sound. The reason for this sound production is the vibration ofthe instrument which creates over – and underpressures in the surroundingmedium, the air. Note that the order of magnitude is really small comparedto the atmospheric pressure (10 5 Pa).Seen in the space this phenomenon is comparable to a wave, like a stonefallingintoapuddle. Soundwillthuspropagateasawavethroughitsmediumand can consequently be characterized by an amplitude, a frequency and awave velocity.Like mentioned above sound waves are induced by a disturbance of the equilibriumin a given point of the elastic medium. They propagate to anotherpoint, in a predictable manner, depending on the physical properties of theelastic medium. Between 20 Hz and 20.000 Hz one speaks of sound. Underthe first value and above the second one a human can not hear it, but itsbody is not completely insensitive to these pressure changes.Different wave types can be distinguished. Sound waves are longitudinalwaves: the particle displacement is parallel to the direction of wave propagation.3

4 CHAPTER 1. FUNDAMENTAL CONCEPTS OF ACOUSTICSFigure 1.1: Sound production by tuning fork. Source: Bruël&Kjær.The wave type produced by e.g. the stone falling into a puddle is calledtransverse wave: the particle displacement is perpendicular to the directionof wave propagation.1.2 Plane sound waves1.2.1 DefinitionBecause of the more simplistic mathematical description with respect tospherical waves, plane waves will first be discussed. However, the physicalrealization is more difficult: an infinite large flat plate must be broughtinto a vibratory motion perpendicular to the plane of that plate. In thisway, it results in a oscillating system of plane regions with alternating over– and under-pressure. The wave fronts (surfaces of constant phase) propagateindeed in a direction normal to the flat pane. The air particles in thedirect surrounding of the plate, and some time later, also further away, movearound their equilibrium in the same direction (normal to the plate). In agiven point the air density ρ is a function of time t, and on a given time alsofunction of the position x: ρ(x,t). The pressure disturbances propagate witha velocity c (the wave velocity, or speed of sound, or also known as phasevelocity).Different parameters are associated to a plane wave:p thepressure fluctuationwithrespect totheatmosphericpressureP 0 causedby sound. Generally, p ≪ P 0 with p = p(x,t).

1.2. PLANE SOUND WAVES 5u the air particle displacement from equilibrium position caused by soundwith u = u(x,t). (A ‘particle’ is a volume that is small enough so thatwithin it , u and v can be considered to be constant).v the particle velocity given by v = ∂u∂tand must not be confused with c.The speed of sound is the propagation speed of the wave, constant forthe continuous medium, for a given pressure and temperature. Theparticle velocity v is variable because the particle (e.g. air) vibratesaround an equilibrium position. On average these particles have a zerovelocity, while the wave phenomenon propagates. The direction of vand c is equal and this explains why sound waves are considered to belongitudinal.Consider a plane wave: along x-axis and independent of y- and z coordinates.In point x = 0 the harmonic motion of a random point can bedescribed by :u(t,0) = U exp(iωt) (1.1)We call this a wave if on position x the same vibrational state holds as inx = 0, but with the proviso that there is a phase difference, caused by thefinite propagation speed of the wave phenomenon. This means that at timet and on position x we have the same vibrations as at time t− x on positioncx = 0.By solving the 1–D wave equation [19] :∂ 2 u∂x 2 = 1 c 2 ∂ 2 u∂t 2 (1.2)one obtains the harmonic solution describing the wave propagation :(u(t,x) = U exp(iωt−i ω )c x = U exp(iωt−ikx) (1.3)withk thewave number ormorespecifically theangularwavenumber definedas k = ω (radians per unit distance).cThe amplitude U is considered independent of x and t, and consequentlythese equations are only valid for undamped propagation. Moreover, thewave equation is only valid for small variations around the equilibrium,which is always the case in acoustics and noise unless so called aerodynamicshock-waves are considered. It can easily be shown that the planewave u(t,x) = U exp(iωt−ikx) is a possible solution of the PDE known as

6 CHAPTER 1. FUNDAMENTAL CONCEPTS OF ACOUSTICSthe wave equation by differentiating two times with respect to the time andrepeating the same with respect to the position x :∂ 2 u= −ω 2 u(t,x)∂t 2∂ 2 u= − ω2∂x 2 c2u(t,x) (1.4)and filling these expressions in the wave equation.If damping is present due to absorption of the medium, the solution hasthe following form:U = U 0 exp(−αu) (1.5)Note that the wave can be considered undamped if propagation of soundoccurs in an (unconfined) air volume. Indeed, the damping of sound at 1000Hz is only 5 decibel per km. One can show that the damping is proportionalto the square of the frequency according to :α = ω2 τc(1.6)With τ the relaxation time (around 0.2 ns for monatomic gases). Consequentlyfor high frequencies damping in air may not be neglected. Concerningthe periodic character, we know that the exponential function withimaginary exponent has a periodicity equal to 2π :1. Time periodicity: u(t + T,x) = u(t,x) with period T. From whichfollows that ωT = 2π and further ω = 2π = 2πf with f = 1 theT Tfrequency.2. Space periodicity: u(t,x + λ) with wavelength λ, from which followsthat λk = 2π. Replacing k = ω c yields : ωλ c = 2π and finally ω = 2πλ c3. Combining 1. and 2. gives us the relation between the spatial andfrequency domain wave propagation parameters :with c the speed of sound.1.2.2 The speed of soundλf = c (1.7)The speed of sound is the velocity at which a perturbation, a wave front,propagatesinthegivenmedium. Itdependsonthepropertiesofthismedium,

1.2. PLANE SOUND WAVES 7Material Speed of SoundGlass 5400Steel 5000Aluminium 5200Nickel 4800Wood 4000Copper 3500Plumbum 1300Platinum 2800Silver 2600Water 1460Seawater 1500Mercury 1407Hydrogen 1260Table 1.1: Speed of sound for common materialsespecially density and elasticity.In gases the following equation is applicable [19] :√ √γP O Kc = = = √ γrT (1.8)ρ 0 ρ 0withK = γP 0 the compression– or bulk modulus for gases andwhere γ representsthe heat capacity ratio and P 0 the atmospheric air pressureT the absolute temperature inKr the specific gas constant√BIn fluids : c = with ρB the compression– or bulk modulus for fluids (in Pa)√EIn solids c = with ρE the elastic– or Young’s modulusThe speed of sound for some common materials, gases and fluids are tabulatedin Table 1.1.

8 CHAPTER 1. FUNDAMENTAL CONCEPTS OF ACOUSTICS1.2.3 The one-dimensional wave equationFollowing parameters are considered :x coordinate of elementary particle in equilibrium.u particle displacement with respect to equilibrium.v particle velocity v = ∂u∂t .ρ the instantaneous value of the fluid density.ρ 0 fluid density in equilibrium (considered constant)s condensationinapoint(defacto: relativechangeindensity). Thisvariableis defined as :s . = ρ−ρ 0ρ 0or ρ = ρ 0 (1+s) (1.9)p the sound pressure P = P 0 +pc wave propagation speedGravitation is not considered and thus ρ 0 and P 0 areconstant. The gas orfluid is assumed to behomogeneous isotropic elastic : there are no dissipativeforces due to viscosity or heat conduction. We limit this study to waves withsmall amplitude such that the condensation s can be considered to be small :ρ−ρ 0 ≪ ρ 0 . While the wave propagates along the x-axis through the fluid,the adjacent fluid layers are also disturbed from their equilibrium position.This displacement u is function of x and t.In order to derive the wave equation we will use three physical laws:1. The mass conservation principle.2. Thermodynamic change of state.3. Newtons equation.Firstly, the mass conservation principle is applied on a volume between xand x+dx and a deformed volume :ρ 0 Sdx = ρSdx(1+ ∂u∂x ) (1.10)

1.2. PLANE SOUND WAVES 9Substituting ρ = ρ 0 (1+s) :assuming that s ∂x∂u ≪ s.ρ 0 = ρ 0 (1+s)(1+ ∂u∂x )1 = 1+ ∂u∂x +s+s∂u ∂xs = − ∂x∂uSecondly, we use thermodynamic change of state (adiabatic assumption :noheattransferbetweenfluidelementandsurroundingfluid). Thisisallowedbecause p ≪ P 0 : ( ) γP ρ=(1.11)P 0 ρ 0with γ = cpc vthe adiabatic constant (around 1.4 for air). The right– hand sideof Equation 1.11 is developed as a Taylor series and only the first two termsare conserved (s ≪ 10 −4 in common acoustic problems). It then follows√:pγPP 0= γs or p = P 0 γs. From the definition of the speed of sound : c = 0ρ 0,we have c 2 = γP 0ρ 0. Rewriting and substituting in the previous equations thisgives (with s = − ∂u ) : ∂xp = −c 2 ∂uρ 0 (1.12)∂xThe fundamental equation of dynamics :dF x = ρ 0 Sdx ∂2∂t 2 (1.13)The elementary force dF x is generated by a difference in pressure : dF x =[p−(p+ ∂p ∂pdx)]S = Sdx After substitution :∂x ∂x∂ 2∂p∂x = ρ 0(1.14)∂t 2If we fill in p, given by Formula 1.12, one obtains (after taking the derivative)the wave equation.It issufficient to findasolution foruinfunctionof xandtinorder tofindtheother parameters of the propagating wave with e.g. the following equations :Pressure: p = −ρ 0 c 2∂u∂x .For an harmonic sound wave(u = Uexp(iωt)exp(−kx)) one has ∂u∂x =

10 CHAPTER 1. FUNDAMENTAL CONCEPTS OF ACOUSTICS−i ω ∂uu en = iωu. It then follows (using the defintion of v and abovec ∂tequation of pressure) :p = ρ 0 cv (1.15)Condensation: s = − ∂u∂xParticle velocity: v = ∂u∂tOne can make the remark that a fluid doesn’t consist of molecules, eachhaving a fixed mean position in space, like we did above in order to derivethe wave equation. Indeed, even in the presence of the sound wave, theparticles are continuously in movement with mean velocities far greater thanthe particle velocity due to the wave.However one has to look at it in a statistical way : the molecules leavingthe elementary control volume are forthwith replaced by other moleculeswhich possesses on average the same properties. Consequently it allows us toconsider particle displacements and particle velocities in our mathematicalapproach. Note that a statistical variable like the sound pressure is moresuited for describing sound waves than the displacement. For this reasonthe pressure is of practical use and also used for measurements. Besides, thesound pressure is almost the only acoustic variable measurable on a relativeeasy manner.In an harmonic wave the displacement u, the wave velocity v as well asthe sound pressure p varies periodically in time and space and all satisfythe wave equation. In acoustics our interest is mainly focused on the soundpressure. The sound pressure p in a plane wave satisfy the wave equation :∂ 2 p∂x = 1 ∂ 2 p(1.16)2 c 2 ∂t 2with solution : p(t,x) = p 1 (t−x/c)+p 2 (t+x/c). The harmonic solution is :p(t,x) = Aexp(iωt−ikx) (1.17)The solutions of this one–dimensional wave equation shows that the amplitudeA is independent of the distance : sound propagating as a planewave does not fade away with the distance to the source. This can lead totroublesome consequences like explained in the two following examples :1. Consider a street in the city with on both sides high buildings. Peopleliving in the higher levels of the buildings are as much bothered by thenoise as people from the lower levels. The reason is that when plentyof cars are circulating in the street it can be seen as a source of planenoise which will propagate upwards as a plane wave. This is not truefor one car in the street.

1.3. SPHERICAL SOUND WAVES 112. In a ventilation system the rooms are connected with the ventilatorby means of long ductwork usually having a constant section. Noisegenerated by ventilation will propagate as plane waves through thesecanals reaching the rooms and thus the users.1.2.4 Acoustic impedance of a mediumThe specific acoustic impedance of a medium, for a given type of wave propagation,is defined as the ratio of sound pressure to particle velocity. For aplane wave with propagation along the positive x-axis :z + = p +v += ρcv +v += ρc = K c(1.18)with use of Equations 1.8 and 1.15. For a plane wave propagating along thenegative x-axis we have z − = −ρc. So for a plane wave, independently ofthe propagation direction, the specific acoustic impedance is a real variable.In the MKS unit system the unit of z is kg/(m 2 sec) or simply rayl (namedafter Lord Rayleigh). Due to the greater role of the product ρc comparedto ρ and c separately its also known as the characteristic impedance or waveimpedance of the medium. At room temperature the impedance of air isapproximatively 400 Rayl.1.3 Spherical sound wavesLet us take a small spherical surface whom all points move radially in a periodicalway, with same amplitude, frequency and phase, around equilibriumposition: this is the monopole or isotropic radiator. The surface will exerta periodic pressure on the fluid in contact with that surface. Consequentlythe perturbation of fluid equilibrium will propagate radially in the shape ofspherical waves. We will assume that contact with the surrounding fluid ispreserved. A lot of acoustic problems are related to this divergent sphericalshaped sound waves, radiated by a point source (limit of the monopole). Togive an example on a distant large enough with respect to a physical dimensionone can consider a machine, a car or aircraft as a point source. Dampingis not considered here. In analogy with plane waves one can obtain (see [19]for the derivation of the equation) :∂ 2 p∂x 2 + ∂2 p∂y 2 + ∂2 p∂z 2 = 1 c 2 ∂ 2 p∂t 2 (1.19)

12 CHAPTER 1. FUNDAMENTAL CONCEPTS OF ACOUSTICSTransformation into a spherical coordinate system one can obtain (see[19]) the following form of the wave equation :∂ 2 rp∂r 2 + = 1 c 2 ∂ 2 rp∂t 2 (1.20)with r = √ x 2 +y 2 +z 2 .Taking rp as one variable we get a spherical wave equation of the sameform as the equation for plane waves. A general solution of this equation, astraveling waves, is thus :rp(r,t) = p 1 (t−r/c)+p 2 (t+r/c) or p(r,t) = 1 r p 1(t−r/c)+ 1 r p 2(t+r/c)(1.21)withthefirsttermrepresenting adivergent spherical wave andthesecondonea convergent spherical wave. Both waves exhibit the same propagation speedc and their amplitudes decreases with increasing distance r, radially fromthe point source. Convergent waves have so to say no acoustical application,while the divergent waves have . Indeed, this latter is present as soon as thedistance from the sound source becomes larger than the physical dimensionsof that source. If the point source produces an harmonic wave one may writefor the divergent wave :p(r,t) = A rexp(iωt−ikr) (1.22)1.4 Cylindrical sound wavesFor a cylindrical line sound source one can show that the solution can bewritten as (see [19]) :p(r,t) = A √ rexp(iωt−ikr) (1.23)An important conclusion concerning the three simple types of sources is thefollowing :For plane sound waves the sound pressures does not decrease with thedistance.For spherical sound waves the sound pressure decreases linearly withincreasing distance.

1.5. SOUND LEVELS 13For cylindrical sound waves the sound pressure decreases inversely proportionalto the square root of the distance.1.5 Sound levels1.5.1 The effective sound pressureSuppose a given source of sound produces sound, i.e. the quickly fluctuatingair pressure makes our eardrum to vibrate which causes through our earand nervous system a sensation of sound. Total pressure can be writtenas : p = p atm + p sound . One could think that (subjectively) if we havethe impression of a constant sound level, intensity or loudness it implies(objectively) a constant sound pressure in time. Nothing appears to be lesstrue. The sound perceived with a constant loudness may be both a pure sinetone and a stochastic sound generated by a source with constant parameter:p(t) is extremely complicated, and yet the human ear have the impression ofa constant loudness. Our purpose is to describe mathematically this soundloudness. Afirst conclusion : theinstantaneous valueandthe algebraicmeanvalue does not matter (this latter is eventually zero). The human hearingsystem is quite insensitive for sharp positive and negative peaks, which maybe cut off. In contrast, it seems to be sensitive to the energy of sound waves.This led to the consideration of the effective– or Root-Mean-Square (RMS)value of the sound pressure, over a certain time interval, as an measure ofintensity :p eff =√1t 2 −t 1∫ t2t 1p 2 (t)dt (1.24)Foranharmonicwave(withDCvalueequal tozero) thisis: p eff = p max / √ 2.As can be seen in the definition the effective value p eff depends of the timeinterval as well as the type of sound. E.g. :1. We listen to a noise which seems to be constant in time. To describethe intensity one can thus use p 2 averaging over a relative small orrelative large time interval – this changes not much to the result of themeasurement. In this case the time interval does not play a major role.2. When a plane flies over one hear the sound surging followed by extinctionduring a specific time interval. If we want to use p eff in thiscase to describe the instantaneous numerical value giving a reasonableimpression of the perceived sound intensity, we would have to average

14 CHAPTER 1. FUNDAMENTAL CONCEPTS OF ACOUSTICSp 2 over a short time period, negligible with respect to the fly over time.In this case the time interval for integration is important.3. Physiological experiments have allowed to see that for the human earthesoundintensityimpressioncansometimenoticeablychangein0.1sec.Consequently this is a maximum value of time integration for variablesound.4. Technical application (the measuring equipment is based on this) : theintegrationinterval istakenrelatively short (e.g. 125ms), such thattheneedleofthemeasuring equipment iscapableofdetecting relative quickfluctuations of the sound pressure; a sound whose variating intensity intime is perceived by the human ear. The measurement system deliversa result that variates in time approximately in the same way. Themeasured values for p eff are more or less located between followinglimits :2×10 −5 Pa < p eff < 200 Pa (1.25)The ratio of the largest limit to the smallest is 10 7 , which is very large.All the common sounds are situated between those limits. For this reason,andalso because earlier onebelieved thatahuman hearsaccordingto the law of Weber–Fechner, i.e. logarithmic, one have introduced thedB-scale (response proportional with the logarithm of the stimulus).1.5.2 The dB-scaleThe dB-scale allows us to describe sound, like a person perceives, in a correctway. The sound pressure level (SPL) is defined as :L p = 10log p2p 2 0= 20log p p 0(1.26)with p 0 = 20 × 10 −6 Pa the reference pressure (it equals the threshold ofhuman hearing). An example of the dB-scale and a comparison with thelinear scale is given in Figure 1.2.The hearing threshold equals 0 dB, the pain threshold is 120 dB. Calculatingwith dB causes often problems because of the fact that we are used towork with the linear scale. Summation and subtraction are best performedby first transforming to the linear scale, then by executing the operation andfinally by transforming back to the dB-scale. For the sum of two values L p1en L p1 :L p = 10log(10 Lp 1 /10 +10 Lp 2 /10 ) (1.27)

1.5. SOUND LEVELS 15Figure 1.2: Some sound values in the linear and dB scale. Source:Bruël&Kjær.Note that when on a given position a certain source produces a sound pressurelevel 10 dB smaller than the sound pressure level of another source, thisfirst source has no big contribution (less than 1 dB) to the sound pressurelevel in that point. This will enable us to perform measurement of soundsources without the need of shutting down all other sources.When multiplying a sound pressure in the linear scale with a certainfactor this results in the addition of a value in the dB scale. Examples (seealso Figure 1.3 :Multiplication with a factor 2 equals an addition of around 6 dB.Multiplication with a factor 3 equals an addition of around 10 dB.Multiplication with a factor 10 equals an addition of around 20 dB.Attention: these rules are only valid for sound pressures p. Later theconcepts of sound intensity and sound power will be introduced. These parametersare proportional to the energy of sound (i.e. ∼ p 2 ) and this is forexample the reason that a multiplication of the sound power with 10 equalsan addition of 10 dB.

16 CHAPTER 1. FUNDAMENTAL CONCEPTS OF ACOUSTICSFigure 1.3: Multiplication in the linear scale equals an addition in dB scalel.Source: Bruël&Kjær.1.5.3 Superposition of two soundsIn this section we will see in more detail how to superpose two sound waves.The resulting instantaneous pressure in a given point is the sum of the instantaneousvalues measured in that point : p(t) = p 1 (t)+p 2 (t). Due to thefactthat oneonlyhear andmeasure effective pressure values, thequestion is:what is the link between the effective pressures p total , p 1 en p 2 . This relationseems to depend on the nature of the sound and the distance between thesources. The total effective sound pressure is given by :√∫1 Tp eff = (p 1 (t)+p 2 (t)) 2 )dt=T√1T0∫ TTwo cases can be distinguished :0(p 2 1(t)+p 2 2(t)+2p 1 (t)p 2 (t))dtIncoherent sources One speak of incoherent sources if∫ T0(1.28)p 1 (t)p 2 (t)dt = 0 (1.29)

1.5. SOUND LEVELS 17InthiscasewecanthussaythatRMS(p total ) 2 = RMS(p 1 ) 2 +RMS(p 2 ) 2 .Examples of incoherent sources :two pure sine tones with differen ferquencies (e.g.two rotating machinesnot rotating synchronous)two independent stochastic soundstwo sources with energy in different frequency bandsSpecial case: iftwo coherent sourcesproducesoundpressure withsameamplitude we have p eff,1 = p eff,2 en dus p 2 eff,total = 2p 2 eff,1 , or in thedB scale :L p,total = L p,1 +3dB (1.30)The total sound pressure level is thus 3 dB higher compared to the caseof only one source present. And thus the noise is not twice as strong(an increase with factor two equals a rise of 6 dB).In general : for n independent sound sources we have that the effectivesound∑pressure in a given point equals the square root of p 2 eff,total =ni=1 p2 eff,i .Example : machines in an enterprise or cars in the street.In general : the n sources are independent but they cause the sameeffective pressure in a given point : p 2 eff,total = np2 eff,1 , or in dB scale :L p,total = L p,1 +10logn dBCoherent sources For coherent sources the following is valid :∫ T0p 1 (t)p 2 (t)dt ≠ 0 (1.31)In this case the total effective sound pressure depends on the phasedifference between the two single sound waves and the amplitudes.Suppose we have two sound waves p 1 en p 2 in a point x and defined asp 1 = Aexp(iωt) en p 2 = Aexp(iωt+φ) (for simplicity we consider thecase were the amplitudes of the waves are equal).One distinguish a few special cases :If φ = 0 we have that p 2 eff,total = 4p 2 eff,1 and for the dB value :L p,total = L p,1 +20logn dB (1.32)If φ = π than follows p 2 eff,total = 0. Considered apart p 1 andp 2 are audible, but together no sound is generated (ant-noise).

18 CHAPTER 1. FUNDAMENTAL CONCEPTS OF ACOUSTICSThis property is used in active noise control. E.g. : anti-noisetechnique in some headphones to reduce background noise as wellas for reducing noise generated by aircrafts in the cabin of theSAAB2000 plane.1.5.4 Types of soundBased on the frequency spectrum some types of sound can be distinguished :Pure tone : A sound characterized by only one frequency and can onlybe generated, approximatively, by a tone generatorMusical tone : (Figure 1.4-above) : It consists of a fundamental withovertones and are together called partials. (Harmonics are partials).The number and the nature of the harmonics define the so-called ’tonecolor’.Chaotic or stochastic sound (Figure 1.4-middle) : (noise, hiss, etc.) Itcovers a wide frequency spectrum (where sounds with a specific frequencyand higher amplitudes than the other, are typical for the machineinvolved), think of ventilators, traffic noise, factory noise, jets,and so on. In acoustics a very detailed analysis will not be performed(cost) but an analysis in 1/1 octave band or 1/3 octave band. Theseare normalized. More detailed analysis e.g. 1/12 octave or even moredetailed are sometimes used in research.Impulse noise (Figure 1.4-below) : is a type of sound which is of veryshort duration, mostly generated by an impact.Sound can also be classified in other ways like considering the change ofamplitude in function of time. This classification will be described in Part IIIof the text where the legislation regarding environmental noise is discussed.1.6 The acoustic intensity1.6.1 DefinitionA sound source delivers energy in the form of kinetic and potential energy,that is transported by the sound wave. Assume we have a ’free field’, i.e. noreflection possible. Consider a plane of 1 m 2 perpendicular to the directionin which we want to determine the intensity of a traveling plane wave.

1.6. THE ACOUSTIC INTENSITY 19Figure 1.4: Some types of sound. Source: Bruël&Kjær.Definition : the intensity I is the sound energy that propagates in onedirection and that is incident on 1 m 2 per sec (or the sound power per unitarea (in Watt/m 2 )). One can easily show for a sound wave along the rdirection that :I r = dE rdtdS= F rdrdtdS= pdSdrdtdS= pv rLet p represent the sound pressure in the considered point (the atmosphericpressure does indeed not deliver energy) and v the particle velocity.We have than that the power per m 2 or intensity vectorĪ(t) : Ī(t) = p(t)¯v(t)(instantaneous values).Important remark : in contrast to the sound pressure p the sound intensityis a vector quantity (considering it being proportional to the velocity). If onewant to know the magnitude of the intensity in a certain direction ē it hasto be calculated with : I(t) = p(t)v(t)cosφ, where φ = ∠(ē,¯v).For an harmonic plane wave we know that (equation 1.15) : p = ρcv. It thenfollows for a traveling harmonic plane wave :I = p effρc = ρcv eff (1.33)

20 CHAPTER 1. FUNDAMENTAL CONCEPTS OF ACOUSTICSNote that a spherical wave behaves like a plane wave if the observer is faraway from the point source (in practice for distances larger than 3λ). For adiffuse sound field, where the waves are in all directions just as strong andindependent, we may find (no proof is given in this text) :I diffuus = p ρc = ρcv eff (1.34)1.6.2 The sound intensity levelDefinition : the sound intensity level (SIL) L I is defined as :L I = 10log I I 0(dB) (1.35)with I 0 = 10 −12 W/m 2 the standard reference sound intensity level.Notethatforatraveling planewavepropagatinginairthesoundintensitylevel is approximately equal to the sound pressure level : L I ≈ L p . Indeed :L I = 10log I I 0= 10log p2ρcI 0met ρc ≈ 412≈ L p1.7 Source power1.7.1 DefinitionDefinition : The sound power is the acoustic power (Watt) delivered by asound source : ∫W = IdS (1.36)with I the intensity in W/m 2 over the elementary surface dS. If I is constantin all directions (nondirectional source) : W = IS.In analogy with the sound pressure level and sound intensity level onecan define the sound power level.Definition : The sound power level (SWL) is defined as :SL W = 10log W W 0(1.37)

1.7. SOURCE POWER 21with W 0 = 10 −12 W the reference level.One have to pay attention to the terms we use because all those differentlevels have the same units (dB).1.7.2 The sound field produced by a point sourceFor a spherical source the source power is W = I4πr 2 , with I the intensityaccording to the radius of this sphere on a distance r from the source. In adistant sound field r ≫ λ we can write I = p2 effρcand thus :W = p2 eff 4πr2ρc(1.38)from which one can get an expression for the effective sound pressure, measuredat a distance r from the source :√Wρcp eff =(1.39)4πr 2With known source acoustic power the sound pressure can be calculatedin a given point. The effective sound pressure decreases with increasingdistance 1 . One may rewrite Equation 1.39 as a function of values in dB.r√412Wp eff = ρc = 400 for air4πr 2⇒ p 2 eff = 412W4πr 2⇒p2 eff 412W=400∗10 −12 4πr 2 400∗10 −12⇒ L p = L W −10log(4πr 2 )For r = 1 one has approximately :L p = L W −10 (1.40)

22 CHAPTER 1. FUNDAMENTAL CONCEPTS OF ACOUSTICS

Chapter 2The human hearing system2.1 Anatomy of the earThe hearing organ is sketched in Figure 2.1 and consists of three parts :the external hearing organ, the middle ear and the inner ear. The externalhearing organconsists ofthepinna (also calledauricle), the external auditorycanalandtheeardrum. Themiddleearconsistsofthehammer, anvil, stirrupand also the eardrum. The inner ear consists of the cochlea.2.1.1 The external earThe external ear consists of the auricle. The use of both ears allows us todetermine the direction where a sound comes from. The brain measures thetime delay in between the sound arriving at both ears. The sound receivedby the auricle is converted in a vibration of the eardrum at the end of theexternal auditory canal.2.1.2 The middle earThe middle ear contains the hearing ossicles : the hammer, anvil, stirrup(see Figure 2.1). The middle ear cavity is connected with the nasal cavityvia the Eustachian tube. This allows to have the same pressure as outside.The ossicles are responsible for the transmission of the sound wave fromthe eardrum to the oval window of the inner ear. The ossicles are attachedto the sides of the middle ear cavity with ligaments and muscles. Whena strong sound stimulant enters (more than 80 dB at 1000 Hz), a muscleattached to the stirrup contracts to restrict the movement : this is calledthe acoustic reflex (Stapediusreflex). This reflex provides the ear with aninternal protection of order 10 dB at low frequent sound : the protecting23

24 CHAPTER 2. THE HUMAN HEARING SYSTEMFigure 2.1: The anatomy of the human ear r : 1) skull External ear : 2)external auditory canal, 3) auricle Middle ear : 4) eardrum, 5) oval window,6)hamer, 7)anvil, 8)stirrup, 12)Eustachian tubeInternal ear : 9) labyrinth,10) cochlea, 11) cochlear nerve. Source : nl.wikipedia.orgeffect decreases with increasing frequency anddisappears above 2000Hz. Thelatency of the reflex decreases with the intensity of the stimulus : it variesfrom a mean value of 150ms with a tone of 80dB to 40ms with a tone higherthan 100dB.2.1.3 The internal earThe inner ear consists of two organs : the half circular channels that providethe balance, and the cochlea, that accounts for the hearing function. Thecochlea consists of a spiral shaped cavity that is divided into two channels bythe cochlear tube : the two channels are filled with a liquid, the perilymphand are connected at the end of the spiral. The upper channel starts at theoval window and the lower channel ends at the round window. When a soundwave arrives on the eardrum, the ossicles pass the motion on to the stirrupthat compresses the oval window and creates a pressure wave in the upperchannel. This wave propagates farther in the upper channel as the tone ofthe sound decreases. The transversal component of the wave (remark thatthis exists in a fluid) exerts its force directly on the cochlear duct where the

2.2. PHYSIOLOGY OF THE EAR 25organ of Corti is located. This is the actual organ that serves to perceivesound. The membrane that separates the upper channel from the cochlearduct is compressed and gives rise to a pressure wave in the liquid of thecochlea (the endolymph), which in turn compresses the basilar membrane onwhich the organ of Corti is situated. The organ of Corti consists of hair cellsinternally arrangedinarowandexternally arrangedin3to5rows. Thehairsof the cells are in direct contact with a heavy membrane, called the tektorialmembrane. When the basilar membrane is compressed, the contact of thehairs with the tektorial membrane will be lost beginning with the externalrows. Every time the contact is broken or recovered, the electrical potentialofthecells ischanged. Thechangesintheelectrical potential aretransmittedtothebrainviathefibresofthecochlear nerve. Inthebrainthey aredecodedand converted into a perception of sound. Due to the interaction between thewaves in the two canals, the maximal displacement of the basilar membranebecomes larger as the incoming tone gets lower. Sharp tones only stimulatea small band near the oval and round window. The maximal amplitude of awave at a certain frequency always stimulates the same hair cells, allowingto precisely distinct between different frequencies.Moreover, the displacement of the basilar membrane (and with this thenumber of hair cells that are in a working state) is proportional to the intensityof the sound : for a non intense sound, only the outer row of haircells will send pulses to the brain. While for a very intense sound all outerrows and eventually the inner row send pulses. The cochlear nerve or rectocochlearpart of the sound perception, is situated directly behind the organ.As happens with the eyes, it is here that the overlap between left and rightnerves takes place. The stimuli come to consciousness in the auditive cortex.This is situated near the temple.2.2 Physiology of the ear2.2.1 The auditory fieldThe sensitivity of the ear is phenomenal. If it were 20dB better, we wouldhave been capable to hear the pressure fluctuations caused by the Brownsemovement of the air molecules! For a tone of 1kHz that we are just ableto hear, the eardrum moves 10 −6 mm. This are distances smaller than thewavelength of visible light : 0.5 µm. The range of audible frequencies of thehuman ear is situated between 20 and 20000 Hz. Tones below 20 Hz arecalled subsonic and those above 20 kHz ultrasonic. The absolute thresholdof hearing is at its lowest for frequencies around 1000 : this is why 1 kHz

26 CHAPTER 2. THE HUMAN HEARING SYSTEMFigure 2.2: The anatomy of the cochlea. Source : Encarta Winkler Prins2004is chosen as the reference frequency for the dB-scale. The pain threshold isvirtually independent of the frequency and corresponds to 130 or 140 dB.Speech is above all a complex mixture of tones, with a frequency spectrumrangingfrom200to4000Hz. Thiszoneintheauditoryfieldiscalledthezoneof speech. The protection of the ear in this zone is of the utmost importancefor a persons the social life (Figure 2.4).2.2.2 Amplification of signals in hearingThe amplification of sound happens in the external ear (external auditorycanal), middle- and inner ear. The amplification in the external auditorycanal relies on resonator-operation and happens predominantly in the speechintelligibility area(Figure2.4). Intheexternal auditorycanal, thatresemblesa open-closed tube, a standing wave originates with if the wavelength of thesound isgiven by λ = 4L, with L ≈ 0.03mthe lengthof the external auditory

2.2. PHYSIOLOGY OF THE EAR 27Figure 2.3: The organ of Corti. Source : anatomie.med.vu.nl andwww.audiologieboek.nlcanal. This means that the resonance frequency of the acoustic system canbe found as follows :f = c4L = 340m/s ≈ 3000Hz (2.1)4∗0.03mBecause the inner ear contains a liquid, there is an impedance mismatchbetween the outer and inner ear. To overcome this mismatch the hearingsystem has two mechanisms that are used to amplify the force that can beexerted on the liquid. The first amplification in the middle ear relies on themechanical amplification of the vibrations of the ossicles. The system of ossicles(hammer - anvil - stirrup) weakens low and high tones and amplifies

28 CHAPTER 2. THE HUMAN HEARING SYSTEMFigure 2.4: The zone of speech. Source : Bruël&Kjær.tones in the speech intelligibility area. Due to a leverage effect, the forcesexerted on the middle ear are amplified with approximately factor three (seeFigure 2.5). Note that although the forces are amplified, the displacementsare attenuated (due to the conservation of energy of the sound wave). Secondly,an amplification of the forces is realised due to the ratio between thesection of the eardrum (where the sound wave strikes) and the oval window(where the sound wave is transmitted to the cochlea).The amplification in the inner ear depends on the frequency of the stimulants,acting on different locations in the cochlea (Figure 2.6). The functioningof the inner ear relies on the propagation of waves on the basilarmembrane. At low frequencies the maximum of the displacement is situatedfurther away in the cochlea (since at any wave length energy is lost,the low frequencies propagate further in comparison with higher tones). Athigh frequencies, the maximum is situated near the oval window. moreover,the stiffness of the membranes in the organ of Corti tuned on the differentfrequency bands that need to be perceived in the different places along thecochlear duct.

2.2. PHYSIOLOGY OF THE EAR 29Figure 2.5: Amplification of the sound by the ossicles.Figure 2.6: Changing cross section of the cochlea to realize a frequency dependenthearing mechanism.

30 CHAPTER 2. THE HUMAN HEARING SYSTEM2.3 Pathology of the ear2.3.1 IntroductionWhen considering hearing disabilities, distinction between conductive hearingloss and perception hearing disorders should be made. The conductivehearing loss concerns all defects that prevent all mechanical conduction ofvibrations to the oval window. For example : constipation of the externalauditory canal, stiffening of the eardrum, concrescence of the ossicles, concrescenceoftheossicles totheside ofthecochlea,... Otosclerosis isacommondisorder where the bone growth hinders the movement of the ossicles, in particularthe stirrup. The surgical procedure in which the stirrup is removed(stapedectomy) and is replaced with a prothese, offers a good chance on fullrecovery of the hearing capabilities. Perception hearing disorder includes alldefects in the cochlea, like : wear of thehair cells, tinnitus, impairment of thenerves. At the moment there is no cure for tinnitus. Devices that look like ahearing aid are sometimes used to generate masking noise to make the disorderbearable. Some medications can be the cause of tinnitus to. Cochlearimplants use an electrostimulation of the cochlea on the round window or inthe cochlea itself. The electronic signal originates from a speech processorand is induced by a coil outside the body on an implanted receiver coil inthe body. This is an aid for people who have a serious hearing disorder orare deaf. It is however still to be considered as the generation of a soundperception far from normal hearing.2.3.2 Development of the ear with ageThe sensitivity of the ear tends to diminish with age, and loss of hearingarises faster at high frequencies in general. The span of the effect of age,called presbycusis, varies strongly from individual to individual. The loss ofhearing at a certain frequency as a consequence of the presbycusis effect isthedifference between theabsolutethreshold ofhearingatthisfrequency andthe ’normal’ absolute threshold of hearing. According to ISO 389 standard,’normal’ thresholds are the median thresholds of a normal hearing, young (20years old) population. Table 2.1 shows the values at the frequencies normallyused in audiometry.In loss of hearing an enormous individual variability exists. For example,atafrequencyof4000Hzthelosscanbe5dBfortheleastsensitiveindividuals(sensitivity = 10%) and 45dB for the most sensitive (sensitivity = 90%).

2.4. THE HUMAN PERCEPTION OF SOUND 31Frequency Threshold125 Hz 45.0 dB250Hz 25.5 dB500Hz 11.5 dB1 kHz 7.0 dB2kHz 9.0 dB3 kHz 10.0 dB4kHz 9.5 dE6kHz 15.5 dB8kHz 13.5 dBTable 2.1: Hearing threshold of a normal hearing young population (20years).2.4 The human perception of sound2.4.1 The phonThe sensitivity of the ear is function of the frequency. Thanks to the experimentsof Fletcher and Munson [15] in the early nineteen thirties thissensitivity was mapped (see Figure 2.7). During these experiments a toneof 40 dB of 1 kHz was presented to the test subjects. Next the frequencywas adjusted and the test subjects were asked to indicate the sound pressurelevel at which the tone sounded equally loud as the original sound at 1 kHz.The resulting curve is the co called 40 dB isophone. The experiment wasrepeated for other sound pressure levels (see Figure 2.7). It follows from thisthat frequency sensitivity depends on the sound levels : at a higher soundintensity the curves get flatter.2.4.2 The sone as measure of loudnessStarting from the results of Fletcher and Munson one could think that forexample a sound of 80 phon has a sound level about ten times as high as asound of 60 phon (remember : a 20dB SPL increase corresponds to a factor10 in sound pressure). In reality, humans experience the sound of 80 phon asfour times louder than 60 phon. Extensive experimental and psychologicalresearch was performed to find a mathematical relation between the loudness(in phon) and the sound level. We can observe from this :loudness level + 10 dB (phon) = loudness X 2

32 CHAPTER 2. THE HUMAN HEARING SYSTEMFigure 2.7: The isophone curves. Source : Bruël&Kjær.Increase/decrease (dB) Experienced change in loudness3 just observable5 Notable difference10 Twice as loud15 Important increase20 Four times as loudTable 2.2: Qualitative experience of loudness with an increase in dB.This relation is valid for 20 phon < L p < 120 phon. This is why the sonescale is introduced to fix a linear relation. An international standard definesthe sone (S) as measure for loudness as follows:S = 2 P−4010 (2.2)A sound of 120 phon is 256 times louder than a sound of 40 phon. Inverselyone has: P = 40 + 33.3logS. The qualitative experience with theincrease/decrease of sound levels is displayed in Table 2.2.

Chapter 3Measuring sound3.1 Introduction: why measure soundIn order to select a useful measuring technique we need to determine whatthe purpose of the sound measurement is. A first important objective can beto determine a sound pollution problem. To do this extend, measurements ofthe sound pressure level are usually sufficient. In such a case the availabilityof a simple, portable measuring system is desirable. It the hindrance ismomentary, one wishes a swift registration of the peak levels. For a longobservation, an automatic averaging and statistical processing is advised andmost of the times required by the legislator. A second objective can be thereduction of noise after the confirmation of nuisance. One speaks of soundsanitation. Mostly, there is a need to examine the frequency spectrum ofthe sound to accomplish this task. To this extend specific measuring devicesare developed. Measurements in frequency bands gives the general pictureof the composition whereas the linear spectrum can be an important aid inlocalizing the source of the sound. The latter can also be done by usingvector intensity measurements, which will not be discussed in this course.A third objective of sound measurements is to investigate if the norms andregulations concerning noise pollution are not violated. In this case, as weshall see in later modules, the measuring parameters as well as the measuringconditions are often prescribed.3.2 The measurement microphoneA measurement system to measure sound pressure consists of a microphone,signal amplifier, conditionings unit and a measuring device. The microphoneconverts vibrations of the air into mechanical vibrations, these are in turn33

34 CHAPTER 3. MEASURING SOUNDconverted in an electric signal. This is amplified and optionally filtered in thefrequency domain. The electrical signal is then read out by the measuringdevice. This reading can be done in several ways (digital display, computerscreen, analog display.The microphone is the critical element in every measuring system forsound. The microphone detects the sound pressure variations and convertsthem into electrical signals. This can be done in several ways:Ceramic or piezoelectrical microphones. The working principle ofceramic or piezoelectrical microphones is based on the properties of thepiezoelectrical material. This material generates an electrical voltagewhen mechanical pressure is applied on it. Ceramic microphones arerobust and not sensitive to moisture and other environmental impacts.Other advantages are their relatively low cost and the fact that noexternal voltage source is necessary.Condenser microphones. The condenser microphone is used to executeprecise measurements. Condenser microphones make use of twoelectrically chargedplates withanair gapinbetween. Oneoftheplatesis a light membrane that moves under influence of the incoming soundwaves. Figure 3.1 displays a construction of such a microphone. Betweenthe membrane and the base plate an electrical charge is createdby a voltage supply. Due to the incoming sound wave the distancebetween the base plate and membrane changes, casing the capacityto change. This results in variations on the voltage over the microphonethat that proportional with the incoming pressure (see Figure3.2). Condenser microphones can be designed to have a sensitivitythat does not change much over time and to have a frequency responsethat is very flat (the sensitivity is the ratio of the measured tensionover the sound pressure, this value is of the order of a few mV/Pa).Moreover they are very insensitive to temperature changes. Due tothis stability condenser microphones are designated to use for precisionmeasurements. Since an notable polarisation tension needs to be appliedover the capacitor, a to high humidity can give problems. The useof a heating element can present a solution to this problem, if lengthymeasurements need to be conducted.Electret microphones an electret is a polymer film with an electricalcharge bound to the molecules. An electret condenser microphone ismade by applying the electret on a perforated metal plate, and shieldit off on the front side with a plastic membrane on which a thin metal

3.2. THE MEASUREMENT MICROPHONE 35coating is applied. Incoming sound waves alter the capacity of the capacitor,thisgivesrisetoanelectricalcurrent.Theelectretmicrophonesdo not need an external polarisation, which is the case for condensermicrophones.Figure 3.1: Layout of a condenser microphone. Source: Bruël&Kjær.3.2.1 Size of the microphoneCondenser measuring microphones exist in a number of standard sizes, thecore number to describe the size of the microphones is the diameter of themicrophone in inch : one distincts the 1/8, 1/4, 1/2 and 1 inch microphones.If the wavelength of the sound to observe is about the size of the diameterof the microphone, the sound pressure will be partially averaged out over thesurface of the membrane and the microphone loses a lot of its sensitivity (seeFigure 3.3). To measure high frequencies, a small microphone will be used.The total incoming acoustic energy will be lower on a smaller microphone,which is disadvantageous for the sensitivity. For a 1 inch microphone onecan easily check that up to a frequency of 8kHz, the frequency response isconstant with an accuracy of 2dB. The sensitivity of such a microphone istypically 50mV/Pa. If one wants to measure higher frequencies, a 1/2 inchmicrophone must be used. This can be used up to 20kHz, but its sensitivity

36 CHAPTER 3. MEASURING SOUNDFigure 3.2: Working principle of a condensator microphone. Source:Bruël&Kjær.is only 12,5mV/Pa. 1/8 inch microphones can be used for measurementsof ultrasonic sound, or when measuring impulse sounds or very loud noises.Themanufacturergivesprecisedataconcerningthesensitivity andmeasuringrange for each type of microphone.3.2.2 The sound field where measurements take placeThe sound field has influence on the measured sound pressure (see Figure3.4). To keep the influence of the sound field as low as possible, differenttypes of microphone were designed :The free field microphone. The freefield is defined asanarea whereno reflected sound waves arepresent. This microphone will compensatethe influence of the microphone on the free field. The highest accuracyis obtained when pointing the microphone to the source.Random incidence microphone for measurements in a diffuse fieldanother microphone is developed that compensates incoming soundpressure from all directions.Pressure microphone A pressure microphone gives a constant frequencyresponse of the sound field, the way it exists, including theinfluence of the microphone itself (no compensation is carried out).These microphones are useful i.a. when the sound pressure on the sideof a cavity is to be measured (e.g. exhaust systems).

3.2. THE MEASUREMENT MICROPHONE 37Figure 3.3: Frequency response of the different standard microphone sizes.Source: Bruël&Kjær.The three types of microphones can also be used in another field thanthe one they are developed for : pressure microphones can be used in diffusefields. If a free field microphone is used in a diffuse field, an electronic correctionmust be carried out. When a random incidence microphone is usedin a free field, the microphone must be turned 70 circ to 80 circ relative to thesource of the sound. A pressure microphone must be placed at a 90 circ anglerelative to the direction of the source. The National American Standards Institute(ANSI) relies on the use of random incidence microphones to composeits standards, the International Electrotechnical Commision (IEC) relies onfree field microphones (see Figure 3.5). In Belgium, norms legislation andregulations prescribe apparatus that comply with the IEC-guideline.3.2.3 Influence of the wind speedIt is common knowledge that wind in the vicinity a microphone producesadditional noise. This pollutes the signal. For measurements in open air, itis therefore advised to use a windscreen (this is a soft foam rubber sphere,as can be seen in Figure 3.6). Windscreens are essentialy transparent in theinteresting frequency range. Typical values are a weakening of 0.5 dB at 5kHz, this increases to 2 dB weakening at 12 kHz. Figure 3.7 displays the

38 CHAPTER 3. MEASURING SOUNDFigure 3.4: Disturbing effect of the microphone on the sound field. Source:Bruël&Kjær.Figure 3.5: IEC en ANSI measuring procedure. Source: Bruël&Kjær.

3.2. THE MEASUREMENT MICROPHONE 39sound power caused by the wind in function of the wind speed. This figuredisplays a very strong sound signal caused by wind speeds above 40 km/u,even when using windscreens. The energy in the noise signal caused by thewind is the highest for low frequencies. At those wind speeds measurementsoutside are better postponed. Moreover, most norms (including the Vlaremlegislation for community noise that is discussed later) prohibit the executionof measurements at speeds higher than 5 m/s.Figure 3.6: Foam windscreens and other accessories for the microphone.Source: Bruël&Kjær.3.2.4 Division of sound in frequency bandsNoise that surrounds us is usually made up out of frequencies spread over thehearing range (20 Hz - 20 kHz). The sound pressure level of this broadbandsignal can be measured in a number of consecutive frequency intervals thatare called frequency bands. Sometimes one prefers frequency bands witha fixed width, bust mostly one uses octave or fractional octave bands. Animportant reason for this choice is that a change of frequency of one octavein the hearing range always causes the same impression of change. Thedifference in frequency between 40 and 50 Hz will be sensed similar as thedifference between 4000and 5000Hzfor example. The standard octave bandsin the audible frequency range have central frequencies (f c ) that equal 31.5

40 CHAPTER 3. MEASURING SOUNDFigure 3.7: Disturbing effect of sound on measured soundlevels. Source:Bruël&Kjær.Hz, 63 Hz, 125 Hz, 250 Hz, 500 Hz, 1 kHz, 2 kHz, 4 kHz, 8 kHz and 16 kHz.The central frequency doubles in every consecutive band. The lower limit ofthe band is given by: f L = √ fc2and the upper limit by: f U = √ 2f c . Insteadof using these exact numbers, the bands were rounded and standardized likein Table 3.1. Third bands or 1/3rd octave bands are obtained by dividingthe octave bands into three separate bands. following relations exist for thirdbands:f tertzcf tertzLf tertzU= 2 1/3 f octavec= ftertz c2 1/6= 2 1/6 f tertzcWhere f tertzL,f tertzc,f tertzUthe third bands and f octaafcare the sub-, center- and upper frequencies ofthe center frequencies of the octave bands.

3.3. FREQUENCY WEIGHTING OF MICROPHONE SIGNALS 41Lower limit f L Center frequency f c Upper limit f U22.4 31.5 4545 63 9090 125 180180 250 355355 500 710710 1000 14001400 2000 28002800 4000 56005600 8000 1120011200 16000 22400Table 3.1: lower-, center- and upper frequencies of the standardized octavebands.3.3 Frequency weighting of microphone signalsMeasuring in octave- and even more in third bands is quite cumbersome.Moreover this results in a whole set of readings per measuring point. Mostlyone tries to limit the number of readings to a minimum with this kind ofmeasurements. To accomplish this one will mostly use an averaged value ofthe different frequency bands. To let the measured values correspond withthe sound perception of the human ear, one will weight the desired soundpressure in the frequency range. To accomplish this different filters are used :the A, B, C and D filer. The A-weighted sound level is accomplished by adjustingthe sound level in every frequency band to the frequency sensitivityof the human ear for soft sounds (40 dB). This is done by a custom filtering.This is standardized (ANSI 1983) and presented in Figure 3.8. The adjustedglobal sound level is displayed in A-weighted decibels (dBA). The B- andC-weighing are defined analogous. They take into account the sensitivityof the human ear at average and loud noises respectively. The filter curvesused for the different weighting schemes are shown in Figure 3.9. Sensitivitymeasurements under different circumstances gave rise to other weightingschemes. D-weighting is used to measure the sound produced by airplanes(very loud noises). In practice one uses quasi only the dBA, independent ofthe sound level. Even at high sound levels dBA is measured instead of dB(B)or dB(C).

42 CHAPTER 3. MEASURING SOUNDFigure 3.8: Inverse of the sensitivity of the hearing at 40 dB and an A-weighting curve. Source: Bruël&Kjær.Figure 3.9: Various standardized weighting curves. Source: Bruël&Kjær.3.4 The sonometerSound level meters are the basic equipment for direct measurements of thesound level, if one is not interested in the frequency spectrum. It can besimple instruments that can be held in the palm of one’s hand and workon batteries. These instruments can easily be used on a site where a noiseproblem might be present (eg. a factory).A typical device consists of a (1/2 inch) microphone, a preamplifier,

3.4. THE SONOMETER 43weighting networks, an amplifier, an RMS rectifier and a meter that displaysthe sound level in dB (see Figure 3.10). A switch allows to chose betweenan A-, B-, C-, D-weighting or no weighting at all. Finally the rectified signalis converted in dB and send to an analog or digital display instrument. Thespeedatwhichthemeterfollowsthechangesinsoundlevel isoftenselectable.In the ’fast’ mode the time constant is approximately 1/8 sec. In ’slow’ modethe time constant is approximately 1 sec. In slow mode, the device averagesthe sound level over the past second. Some devices contain octave or 1/3octave filters, others have an ’impulse’ and a ’peak hold’ feature, that canmeasure signals with a steep rise or that can hold the maximum of a soundsignal in a certain period.Figure 3.10: Build up of a sonometer. Source: Bruël&Kjær.According to their accuracy, three types of sound level meters are specifiedby the ANSI (American National Standards Institute) and the IEC(International Electrotechnical Comission):Type 1: precision devicesType 2: devices for general useType 3: inspection devicesA laboratory reference device is called a device of Type 0. The exactaccuracy of the sound level measurement is of course dependent of several

44 CHAPTER 3. MEASURING SOUNDfactors. In general one can state that with a Type 1 meter the error will beless than 1 dB. The accuracy of a Type 2 device is approximately 2 dB.3.5 Calibration of measurement systemsA microphone is usually accompanied with a calibration chart upon delivery.On this map the frequency sensitivity is mapped (see Figure 3.11). Thereexist numerous calibration methods for microphones or measuring systemsa a whole. One has recorded that when measuring sound pressure levels,the best results are obtained when a pistonphone is used for the calibrationof the system (see Figure 3.12). A pistonphone (piston calibrator) consistsof an engine that moves a few pistons back and forth. The calibration isdone by placing the junction piece of the pistonphone over the microphoneand switching on the device. A pistonphone will typically generate a signalof 250 Hz at 124(±0,5) dB. Oscillator based soundlevelcalibrators are light,small and battery-backed. The electrical oscillator controls a piezoelectricalelement that causes a membrane to move. The sound pressure level thatis generated is 94 ± 0.3 dB. The resonance frequency typically is 1000Hzsince at this frequency possible weighting has no influence. his frequency isstabilized by the Helmholtz resonator with a natural frequency of 1000Hz,that is formed by a cavity behind the membrane.3.6 Presence of the observerThe presence of the instruments and the observer in the sound field willperturb the measurement. If measurements in a diffuse field are executed,the error will usually be small. If one wants to measure in the proximity ofa source, the observer shall obviously not be in the direct line between thesource and measurement device. Preferably the instrument is placed on atripod and the observer steps back at least half a meter behind and sidewaysof the instrument. Octave band or small band measurements are much moresensitive to the presence of the observer. Usually in this case the microphoneis mounted on a tripod and connected with a cable of at least half a meter tothe other equipment. When measuring in an anechoic room, all equipment(except for the microphone) and the observer shall be placed outside theroom.

3.7. BACKGROUND NOISE 45Figure 3.11: Calibration sheet accompanying a microphone. Source:Bruël&Kjær.3.7 Background noiseWhen measuring sound caused by a certain source, all other sounds presentare considered as background noise. If the level of the background noiseis more than 10 dB lower than the total sound pressure level, it can beneglected. If it is less than 10dB lower, a correction is necessary. Assume wewant to determine the sound level L S of a source, situated in an environmentwith a background sound level L N . The combined sound level (background+ source) is L C . L N and L C are measured and L S is the value we want todetermine. Since the source and the background noise are not correlated, theaveragequadraticsoundpressuresofthecombinedsoundandthebackgroundnoise need to be subtracted to obtain the source term. Taking into accountthe definition of the sound pressure level we find:( )L S = L C +10log 1−10 −L C −L B10(3.1)

46 CHAPTER 3. MEASURING SOUNDFigure 3.12: pistonphone for the calibration of a microphone. Source:Bruël&Kjær.3.8 Quantitative parameters3.8.1 The equivalent sound pressure levelTo characterize sound that highly varies in time, one introduces the equivalentsound level. A constant sound at this level contains the same acousticenergy as the highly varied sound. The equivalent sound level is obtained byaveraging the average quadratic sound pressure over the desired time intervaland converting it again to dB. From the definition of the sound pressure levelone obtains:this gives :p 2 rmsp 2 0( ) p2L eq = 10log rmsp 2 0= 10 Lp/10 (3.2)( 1= 10logT∫ T0)10 Lp/10 dt(3.3)With L eq the equivalent sound level (dBA), p 2 rms the time average of theaverage quadratic sound pressure and T the time over which the averaging

3.8. QUANTITATIVE PARAMETERS 47operation takes place. The integration in Equation 3.3 is replaced by a sumover a set of N measurements in practice:(1L eq = 10logTN∑i=110 L i/10)(3.4)Theequivalent soundlevel isdirectlymeasured withtheaidofamicroprocessorcontrolled sound level meter. This can usually be programmed to executeand record a whole set of measuring cycles over a period of 24 hours.3.8.2 Sound Exposure LevelThe sound exposure level (SEL) is used to characterize a single event, bothin sound level and duration. The SEL is defined as:∫ TSEL = 10log( 10 L/10 dt) (3.5)0with T the time measured in seconds. The SEL can also be measured withan integrating sound level meter. The SEL can be used to characterize thenoise produced by say, a certain machine action.A dosimeter or noise exposure meter is an instrument that is designed tomeasure the accumulated noise exposure of workers in an industrial environment(like dosimeters exist for radiation). The dosimeter is a compact device(see Figure 3.13) with an integrating sound level meter that can be worn byworkers during their normal activities at work. Usually the dosimeter hasan internal memory to track the sound exposure of several workers. Apartfrom the sound exposure levels in dBA, the percentage of the allowed leveland the peak level is displayed. Also the data and duration of the measuringperiod are registered.3.8.3 Statistic sound levelsIn lots of real life situations the sound level will vary strongly in function oftime. When registering such a sound over an extended period, it is difficultto interpret. Apart from often continuously present sound, there is a wholeset of interferences. Because of this the sound can be registered in a statisticway. Per time period, all sound pressure levels are registered. This can bestatistically displayed in a statistic or cumulative distribution. These cumulativemeasured values are also called the fractional sound pressure levels.

48 CHAPTER 3. MEASURING SOUNDFigure 3.13: Dosimeter. Source: Bruël&Kjær.Typical cumulative distributions are the L 99 , L 95 , L 50 , L 10 , L 5 and L 01 distributions.L x indicates that during x% of the time, a sound pressure levelis present larger than or equal to the indicated value. For example; L 95 = 60dB indicates that 95% of the time, the sound pressure level is at least equalto 60dB. L95 and L 90 can be interpreted as the sound pressure levels thatare continuously present, whereas L 10 and L 05 indicate sound pressure levelsthat are caused by accidental noises (eg. passing vehicles).3.8.4 The Noise Rating valueNoise pollution is related to the loudness and the frequency spectrum of thesound. This is the case because of the following reasons : a) high tones proveto contribute more to the nuisance of sound than the low tones; b) whendealing with noise one wants to track the source, and this is only possiblewith a frequency spectrum analysis. One has searched for a better one digitsystem, thatalso takes into account thespectrum. Inthis wayonegetsthesocalled ISO-limit curve for noise, also called the N.R. or Noise Rating curves(see Figure 3.14), presented by Kosten and Van Os. These are prescribedfor e.g. the determination of noise of ventilators and HVAC units. Theydisplay an octave band level (dB) in function of the frequency. They areenumerated according to the number of dB sound pressure in the 1000Hz

3.8. QUANTITATIVE PARAMETERS 49octave band. One only needs to analyse the noise in the octave bands andconnect themeasuring pointsto getapolygonal figure, this figureneeds to besuperimposed on the NR-curves. The NR number of the lowest not crossedcurve is a measure for the noise pollution caused by that noise. One mayinterpolate. The value obtained, has to be corrected to take into account theduration of the disturbance, the season, the surroundings etc. In the ISO-1996-standard all these notions are fixed. Tolerable limits for the sound thatmay enter a living room, bedroom, bureau, hospital etc. are also proposedin this standard. Or the sound that may be caused in a factory, central, at atransformation station, etc. A few examples, as presented in the ISO-1996-standard. - in a bedroom : NR 25, concert hall : NR 30 - in offices : NR 40,typing pool : NR 55 - in a factory : NR 85Figure 3.14: Noise rating curve.3.8.5 The nuisance of fluctuating soundThe NR method is interesting to represent the nuisance of a sound by asingle value, taking into account the frequency spectrum of that sound. Neverthelessthis is only valid for a sound with constant magnitude in time. Inlater research one has tried to express the nuisance of a fluctuating sound bya single value, assuming the nuisance is not only dependant of the averageloudness of the sound (L eq ) but also of the changes the loudness is undergoes.

50 CHAPTER 3. MEASURING SOUNDFor example, cars and airplanes that pass by repeatedly will not raise theaverage sound level L eq much but are annoying because of the repeated risingand fading away of sound. In other words, the frequent variation comparedto the background noise. Robinson proposed a measure: Noise PollutionLevel or N.P.L. : NPL = L eq +2.56σ. with L eq the energetic time averageas discussed above, and σ the standard deviation, that is to say, a statisticmeasure of the variationsof the sound. The larger these variations, the largerσ. There exists a very good correlation between the values obtained for NPLand the subjective nuisance of the fluctuating sound. For airplanes specialmodels exist. The noise loading is expressed as: L Amax +blogN +c, with Nthe number of flybys within a certain time interval, and a, b and c representconstants.3.9 The intensity meterIn Chapter 1 the notion sound intensity was introduced and it was shownthat the acoustic intensity I x in a direction x is given by : I x = v x p, where v xrepresents the particle speed of the sound wave in the x direction and p thesound pressure. The sound pressure can simply be measured with a microphone,but measuring the particle speed is far more difficult. This vectorialquantity can however be measured with the aid of a derived quantity :F x = ma⇒ ρ ∂v x∂t = −∂p ∂x⇒ v x = − 1 ∫ ∂pρ ∂xIn reality the derrivative of the pressure with respect to the distance is calculatedby discretization :I x = p.v x= − 12ρ∆r (p A +p B )∫(p A −p B )dtwhere p A and p B represent the sound pressure on two neighbouring locations.This discretized equation is used to calculate the sound intensity with theaid of the intensity meter (see Figure 3.15). This measuring device consistsof two microphones spaced out over a fixed distance with a so called spacer(a few centimetres).The use of the intensity meter offers some advantages :

3.9. THE INTENSITY METER 51Since the intensity is a vectorial quantity is one can determine thedirection in which the intensity is the largest. This means the intensitymeter can be used to localize sources of sound (One can ’scan’ wherethe sound comes from so to speak).It will be shown further that the intensity meter can also be used tomeasure the sound power of a source (see the next paragraph). For thispurpose the intensity meter has a few important advantages :– Thebackground noise canbeeliminated (under the conditionthatit is stationary).– Onecandefinearandomsurfacesurroundingthesourceofasound(instead of a simple spherical surface).– One can measure closer to the source (where the sound waves arenot necessarily in plane or spherical).There are a few issues that require attention when using an intensitymeter however :Forafixed distance between the microphones, the intensity meter hasarather limited frequency range where the measurements are valid. Theupper limit is given by f U = c (for a distance D = 0.05 this comes4Ddown to f U = 1700). At low frequencies the value derived from thetheory is still correct, but noise present in the measurement will resultin an incorrect measurement.The direction of the probe is of great importance. To measure thepower of the source, the intensity probe has to be held perpetual onthe defined surface at all times (this is not the case for an intensitymeter that is not directional).The cost of an intensity meter is much higher than that of a sonometer.The calibration of the probe is also a lot more devious (the twomicrophones must be matched perfectly.The error on the measured intensity depends on the distance r betweenthe microphones of the intensity meter and the frequency. Assume the instantaneouspressure on a certain point in time is given by :p(x) = p m sin(kx) (3.6)with p m the amplitude, k the wavenumber and x the coordinate of themeasured midpoint between the microphones. The exact expression for the

52 CHAPTER 3. MEASURING SOUNDderivative of p is :∂p∂x = p mkcos(kx) = kp m (3.7)The approximation p A −p B is given by :p A −p BrThe relative error equals := p m(sin(kr/2)−sin(−kr/2))re = p mk −2p m sin(kr/2)/rp m k= 2p msin(kr/2)r= 1− 2sin(kr/2)kr(3.8)(3.9)Example : suppose one uses an intensity meter wit a 6mm spacer to measurethe intensity at 12kHz. It can be calculated that k = 217.9m −1 and thereforekr/2 = 0.65 and e = 0.07. The relative can be seen to equal 7%. This errorwill increase rapidly when using a bigger spacer.3.10 Measuring sound sources3.10.1 Measurements in an anechoic half-spaceAn anechoic half-space is a room that is confined (usually at the bottom)by a hard surface, that reflects the sound waves (see Figure 3.16). Along allother walls there is in principle no material border, or, the sound waves arecompletely absorbed (and not reflected). This anechoic half-space is realisedoutside on a hard concrete surface (without buildings or other objects inthe near surroundings), or inside in an acoustical dead room with a hardfloor. The measurements of the sound power in an anechoic half-space areconducted as described in the ISO standard 3745 [4]. The sound source isplaced on the hard surface. The measuring points, n in number (6 or 8)are placed at a distance far enough from the source to guarantee that themeasurements areconducted inthefarfield(seeFigure3.16). Inpracticethismeans that the measuring points are placed at a distance of at least threewavelengths from the source. Moreover the measuring points spaced outover the half-space (on a half spherical surface) in such a fashion that everypoint is concerned with an equal part of the surface S i . This means that :nS i = 2πr 2 . If the machine radiates non-omnidirectional sound, the variousmicrophones will not measure equal sound pressure. One will therefore takeinto account the ’spatial average effective’ pressure p p in the expression ofthe power W :W = I2πr 2with I = p2 mρc(3.10)

3.10. MEASURING SOUND SOURCES 53Figure 3.15: An intensity meter.We can use the above expression because there is a free field above the hardsurface. We switch to reduced quantities:WW 0= 1 W 0p 2 mρc 2πr2p2 0p 2 0= p2 m2πr 2p 2 0becausep 2 0W 0 ρc = 1

54 CHAPTER 3. MEASURING SOUNDThe sound power level can therefore be determined with the following expression:L W ≈ L pm +20logr +8dB (3.11)where L pm is determined in the following manner : L pm = 10log p2 m. Thep 2 0averaged sound pressures are calculated in the following way :p 2 m = 1 ∑p 2 inS S i. (3.12)iThe measurements are conducted in all normalized frequency bands (octavebands).iFigure 3.16: Anechoic half-space.3.10.2 Measurements in a full anechoic roomThe more fundamental measurements are conducted in an acoustic deadroom, where the microphones are placed over a complete spherical surfacesurrounding the source. In this case the sound level is given by :L W = L pm +20logr +10log4π ≈ L pm +20logr+11dB (3.13)

3.10. MEASURING SOUND SOURCES 553.10.3 The comparison methodIn the ’comparison method’ one uses a reference source which is normalised.The method itself is also standardized in many industries. The test is conductedin a so called acoustic hard room, since one does not usually haveaccess to an acoustic dead (anechoic) room. The reference source can generatefor example a power L ′ W . Firstly, one has to install multiple microphonesspaced out in the room and not to close to the machine (in the far field). Onemeasures the sound pressure levels L pi and the spatial averages L pm of thesound radiated by the unknown source (use Equation 3.12). Secondly, onethen replaces the machine with the reference source and one measures L ′ pm inan identical fashion (microphones on identical positions). In each frequencyband the following equations hold true : L W = L pm +C and L ′ W = pm+C L′(where c is a constant that is the same for the two measurements) The unknownpower can be calculated from :L W = L ′ W +(L pm −L ′ pm ) (3.14)3.10.4 Power measurement with an intensity meterDue to the fact that the measuring locations for the described comparisonmethods are located in the far field, that method is not applicable whendifferent objects are placed close to each other. In this case one can use anintensity meter to measure the sound power. The following procedure mustbe used to do this (ISO 9614) :Define a random surface S that includes the source. This does not haveto be placed in the far field but can be situated close to the source.Measure the intensity I i in N discrete points on the surface S.Calculate the power level : L W = 10log ∑ N W ii=1 W 0with W i = I i S i .Instead of discrete measuring locations an alternative method can beused where the intensity meter scans in a continuous fashion over the definedsurface (the so called sweep method, described in ISO 9614-2). Care must betaken that the sweep speed is as constant as possible, moreover the intensitymeter must be held perpendicular to the surface.

56 CHAPTER 3. MEASURING SOUND

Part IINoise control57

Chapter 4Sound AbsorptionAll(construction)materialshave, toagreaterorlesserdegree, thepropertyofsoundabsorption: concreteandstoneabsorblesssound, woodandfibreboardmore. It often occurs that too much sound is reflected, and so one can hearechoes in a room. One can decide to cover certain boundaries of the room,with materials that better absorb the sound, e.g. in homes or offices :Acoustic tiles on the ceilingAcoustically absorbing plates against the wallsCarpet on the floorCurtains in front of the windowsOne should pay attention to the fact that these sound absorbing materialsserve to attenuate the sound reflections. They are not used to improve soundinsulation, asisoftenthought. Thesoundinsulationofanabsorbing materialis quite small, and the misconception probably originates from the fact thatgood thermal insulating materials like glasswool and rockwool, are also goodsound insulating materials.4.1 Acoustic transmission between two mediaIn practice it never occurs that an acoustic wave, generated by an acousticsource, propagates exclusively in one medium. Usually the wave will propagateon to a second medium (e.g. gas/fluid, gas/solid, etc.). In this sectionwe will present a model which allows us to study to which extent energyis reflected, and to which extent energy will be transmitted to the second59

60 CHAPTER 4. SOUND ABSORPTIONmedium. We will start this study with the simple case of normal incidenceof a sound wave.4.1.1 Normal incidenceLet us consider a plane sound wave p i (t,x) that impinges on the interfaceof two media (each medium is semi-infinite). One part of the energy willbe reflected in wave p r and another part will be transmitted in wave p a (seeFigure 4.1). Given all the energy is either reflected, either absorbed, one canwrite :I i = I a +I r (4.1)with I i , I a and I r the incident energy, absorbed energy and reflected energyrespectively (the transmitted energy is neglected because in practicethe transmitted energy is various orders of magnitude smaller). We can alsouse the following dimensionless coefficients: absorption coefficient a = IaI iandreflection coefficient r = IrI i, so : a = 1−r.There are two continuity conditions which need to be fulfilled at theinterface x = 0 at each point of time t :Total sound pressure of Medium 1 needs to be equal to total soundpressure of Medium 2 :p i (0,t)+p r (0,t) = p a (0,t) (4.2)Total normal speed of the particles of Medium 1 needs to be equal tothe normal speed of the particles of Medium 2 :v i (0,t)+v r (0,t) = v a (0,t) (4.3)Physical contact between the two media is expressed by these two conditions:the vibration movement is completely passed on. For the sound wavein positive and negative direction we can write : v(x,t) + = p(x,t) +andzv(x,t) − = p(x,t) −with z = ρc the characteristic impedance. Equation 4.3zcan be rewritten using pressures :1z 1(p i (0,t)+p r (0,t)) = 1 z 2p a (0,t) (4.4)By eliminating the transmitted pressure wave p a in Equations 4.2 and 4.4we can find the the ratio of the reflected pressure to the normal incidentpressure :p r (0,t)p i (0,t) = z 2 −z 1(4.5)z 2 +z 1

4.1. ACOUSTIC TRANSMISSION BETWEEN TWO MEDIA 61By elimination of the reflected pressure wave p r from Equations 4.2 and 4.4we can find the ratio of the transmitted pressure to the normal incidentpressure :p a (0,t)p i (0,t) = 2z 2(4.6)z 2 +z 1From these last two equations we can calculate the coefficients of absorptionand reflection :a = I aI i= p2 az 2z 1p 2 iso :r = I rI i= p2 rz 1z 1p 2 ia = 4z 1z 2(z 1 +z 2 ) 2r = (z 2 −z 1 ) 2(z 1 +z 2 ) 2If the acoustic impedances z 1 and z 2 are frequency independent, so will be aand r, and they can be used for various waveforms.In practice, one can distinguish three cases :z l ≪ z 2 e.g. for the transition from gas to solid. In that case :a ≈ 4z 1z 2(4.7)and r ≈ 1, which means that only a small amount of energy will penetratethe solid and most energy will be reflected to the gas.z 1 = z 2 : Now a = 1, r = 0, which means that all energy incidenton the interface between two media, will be transmitted to the secondmedium. No energy will be reflected to the medium from which thewave is generated. This means that a so-called ’impedance match’ isrealized.z l ≫ z 2 (e.g. solid to gas). The same result is obtained as in the firstcase, because all the expressions of a and r are symmetrical in z 1 andz 2 . There is only small transition of acoustical energy and most energyis reflected.

62 CHAPTER 4. SOUND ABSORPTIONFigure 4.1: Transmission between two media.Example: interaction air/water: z 1 =415 rayl, z 2 = 1.48 × 10 6 rayl. Inthis case a = 0.00112 and r = 0.99888.Apparently the impedances are not adjusted and there is strong reflection.The fact that in Cases 1 and 3 there is mostly reflection, does not mean thatthe pressure waves form the same image in these two cases. We will nowconsider this. The total pressure in Medium 1 is given by :p(x,t) = Aexp(iωt−ikx)+Bexp(iωt+ikx) (4.8)with A and B are the amplitudes of the incident and reflected waves (noticethat thedirection ofpropagationof the reflected wave changes and that thereis a complex amplitude because a phase shift with respect to the referencemay occur). Again we distinguish two cases :Case 1 : (z 1 ≪ z 2 ) so B = A. This allows us to rewrite the pressure :p(x,t) = Aexp(iωt−ikx)+Aexp(iωt+ikx) = 2Acos(kx)cos(ωt)(4.9)This is a standing wave with amplitude 2Acos(kx). On the interfacex = 0, cos(kx) = 1andsotheamplitudeis2A. Therewillbeadoublingof pressure (also see Figure 4.2).Case 2 : (z 1 ≫ z 2 ) so B = −A. This allows us to rewrite the pressure :p(x,t) = Aexp(iωt−ikx)−Aexp(iωt+ikx) = 2Asin(kx)cos(ωt)(4.10)

4.1. ACOUSTIC TRANSMISSION BETWEEN TWO MEDIA 63This is a standing wave with amplitude 2Asin(kx). On the interfacex = 0, sin(kx) = 0, so the pressure is also equal to 0. (also see Figure4.3).Figure 4.2: Amplitude of the standing wave at transition from low to highimpedance.Figure 4.3: Amplitude of the standing wave at transition from high to lowimpedance.Fromtheabsorptionandreflectionexpressionsinfunctionoftheimpedances(see Equations 4.7), one can deduce that the impedance of a good acoustic

64 CHAPTER 4. SOUND ABSORPTIONabsorbing materials is close to that of air. Seen that this impedance is rathersmall (∼ 400 rayl), it is not easy to find solid materials which absorb enoughsound. However, there exist alternative solutions for the physical realizationof sound absorption, based on other phenomena :A plate on a layer of airHelmholtz resonatorPorous acoustic absorbing materialsFollowing sections will give an overview of these three methods.4.2 Realization of acoustic absorption4.2.1 Plate on an air layerA plate on an air layer belongs to the category of resonant absorption means.Onefixes aplate (plywood, chipboard, sheet metal, hardboard, plasterboard,etc.), using wooden slats or profile irons, at a distance of some centimetersin front of a hard wall (see Figure 4.4). The plate, together with the airbehind it, constitutes a mass-spring system. The plate represents the mass,while the air represents the spring element. In fact the plate has also someresilience, but it can be shown that its influence is negligible once the plate isof a certain size (starting from 1 m x 1m). The method of attachment of theplate is therefore almost of no importance, i.e. one may reason on a highlysimple physical model: a plate freely suspended on an air cushion of a fewcm thickness. The wave length of sound is supposed to be much bigger thanthe thickness of the air cushion, so no wave phenomena occur. Let :m mass per square meter of panel surface,d damping per m 2 ,k the stiffness coefficient of the air layer behind the plate,p the excitation force per m 2 , i.e. the sound pressure incident on the plate.then one can find for this model with one degree of freedom :mẍ+dẋ+kx = p (4.11)or by writing the equation in function of the particle velocity v :∫m˙v +dv +k vdt = p (4.12)

4.2. REALIZATION OF ACOUSTIC ABSORPTION 65For harmonic signals : ˙v = iωv and ∫ vdt = 1 v and thus Equation 4.12 caniωbe rewritten :iωmv +dv +k viω = p (4.13)Thus, the impedance z = p of the system is given by :vz = iωm+d+ k(4.14)iωOne can show that the stiffness k of the air layer is given by k = γP 0D(no proof is given in this text), with P 0 the atmospheric pressure and D thedistance between plate and wall. The resonance frequency of the mass-springsystem can be deduced from Equation 4.13 :f 0 = 1√k2π m = 1√γP0(4.15)2π mDIn the practical case of a light panel, for example, this gives, with m =4kg/m 2 and D = 0.04 m, f 0 = 150 Hz. Now when a sound wave hitsthe panel, it will vibrate at the frequency of the sound. When this forcedfrequency is in the vicinity of the eigenfrequency of the panel, calculatedabove, shall this strongly vibrate on the air spring. All sorts of friction losseswill then occur (internal losses in the panel due to the deformation, frictionof the panel on the slats, etc...) which cause the loss of vibrational energy,i.e. sound energy will be absorbed. Moreover when rockwool or glass woolmats are applied in the air gap, than this will augment the dissipation ofenergy, making the sound absorption increased in a wider domain aroundthe eigenfrequency of the panel. I.e. the damping term d can be consciouslyadapted to the needs. When the expression of the impedance is put intothe expression of the absorption, one is capable to calculate the acousticabsorption coefficient of a given material as a function of frequency. Theexperimentally obtainedvalueofaisusuallysmaller, andtypically nothigherthan0.5 (generally 0.3 to 0.4) andthe bandwidth amounts to several octaves.The eigenfrequency is low, thus a panel on an air layer is typically applied toabsorb low tones. Absorption at low frequencies is often absent in modernbuildings, one canencounter absorption of highfrequencies in these buildingsdue to, for example, porous fiber board, which is applied as lost mold of theceilings.4.2.2 Helmholtz resonatorBy applying a large number of holes (round, elongated, ... ) to a panel, itsacoustic properties are changed. When a sound wave impinges on a perforatedpanel, the incident sound wave will not vibrate the mass of the panel

66 CHAPTER 4. SOUND ABSORPTIONFigure 4.4: Schematic representation of a plate on an air layer.alone, but will also excite the mass of the air in the holes : these small masseswill start to resonate on the air spring behind it : this phenomenon is calledthe Helmholtz resonator. The Helmholtz resonator originally consisted ofa small space, filled with air (see Figure 4.5). There is an opening with aneck, which forms the connection with the environment. (One can think forexample of a bottle). The air in the hollow space takes the role of an airspring, in which the mass of the air in the neck will start to vibrate. Thereis a clear agreement with the perforated panel.The realization of noise absorption is similar to the plate on an air layer,where in this case, a column of air resonates on a volume of air. It is clearthat the mass of the vibrating air is much smaller than the mass of the(perforated) plate. The mathematical model that was previously created,remains valid, but m has a different meaning and a much smaller numericalvalue. In practice, the resonance frequency is 7 to 10 times higher. Moreover,the bandwidth B within which sound can be absorbed well, is slightly larger.Indeed, the quality factor of the oscillation circuit is :Q = ω 0md+ρc(4.16)and is thus greatly reduced because of the small numerical value of m in air.The bandwidth B is inversely proportional to the quality factor Q. Even

4.2. REALIZATION OF ACOUSTIC ABSORPTION 67with perforated panels, one can adjust the friction term d as desired, e.g.by applying rock wool or glass wool in the air layer behind it. Moreover,there are also products available on the market that approach the resonatorof Helmholtz in shape : very thick embedded, sawed or milled wood fiberpanels. Indeed, the air mass in the holes, cuts or milled grooves can vibrate,while energy is dissipated in the porous fiber material. They absorb mainlyin the acoustic middle frequency range.N.B.: The air behind the big plate, as well as the air in the Helmholtzresonator undergoes compression and expansion as a whole, i.e. it is assumedthat no wave phenomena occur (λ > characteristic size).Figure 4.5: Schematic representation of a Helmholtz resonator.4.2.3 Porous acoustic absorbing materialsConsider a porous material which consists of fibers (diameter 2 to 20 µm)that are random oriented, and bonded to each other at their contact pointsusing a resin. Frequently used fiber materials for acoustic absorption areglass or mineral materials. Notwithstanding the specific mass of the glassor mineral fiber (approximately 2400 kg/m 3 ) the mass of the bulk porousmaterial is only between 30 and 200 kg/m 3 (average of about 100 kg/m 3 ).The porosity is thus very large : the ratio of pore volume to total volumeamounts to about 95 to 98%. The pores are all in connection to each other,

68 CHAPTER 4. SOUND ABSORPTIONand one may therefore say that the air in these pores participates completelyto the sound movement if a wave is incident. Viscous friction losses in theair occur due to the vibrating movement of the air and furthermore alsoimpulse losses due to the constrictions, dilations and turns along the manyfibers. These losses mainly occur athigher frequencies. Moreover, theair willbe alternately compressed and relaxed and therefore experience temperaturefluctuationswhichwill giverisetoheatexchange withthefibers. Thiscreatesthermal losses, and these tend to occur at lower frequencies. The result of alloccurring losses is that the compressibility modulus K and the propagationvelocity c are complex quantities in porous media. From the complex natureof c follows that the wave is damped (see above). A first model to describethe sound propagation in porous material, is that of the quasi-homogeneousabsorber in which it is supposed that fibers and pores are evenly distributedover the entire volume and that their dimensions are small compared to thewavelength of the sound. A second model is that of Rayleigh in which theporesarerepresentedbyalargenumberofcylindricaltubesofsmalldiameter,parallel to the wave propagation direction. There are many other theoreticalmodels. We will not discuss the mathematical formulation of these modelshere.Experimental research of Delany and Bazley on a very large number ofporous materials, and statistical processing of the measurement results, hasled to following practical model for the wave impedance z = r +ix :r = z 0 (1+0.0571( ρ 0fR s) −0.754 )x = z 0 (−0.087( ρ 0R s) −0.732 )with z 0 = ρ 0 c, f the frequency and R s the specific air resistance in Rayl/cm.The above expression is valid for 10 ≤ f R s≤ 1000.According to C.W. Kosten it is possible to use the model of impedanceof an air column for the porous material :z = −iρccot ωl(4.17)cwhere ρ and c are complex quantities, and l is the thickness of the porouslayer. At increasing frequency, z will, due to the cotangent function, runthrough an infinite series of zeros and poles i.e. anti-resonances and resonances.The art of sound absorption consists of adapting as good as possible thevalue of impedance of the absorption means to the impedance ρc of the air,within the desired frequency range. In the selection of a porous acousticmaterial, the following factors are taken into account :

4.2. REALIZATION OF ACOUSTIC ABSORPTION 69Thenarrowertheporesare,thestrongerwillbetheairfriction, thusthestronger the damping, i.e. absorption. In order to measure the acousticabsorption of a porous material an experiment can be conducted tomeasure the airflow through the material as shown in Figure 4.6. Thespecific air resistivity R s is a measure for this, defined by R s = −1vIt seems obvious that R s must be sufficiently large to achieve dampingand thus absorption. On the other hand R s should not be too large,becausethentheporeswillbecometoonarrowandonlyasmallfractionof the incident intensity will penetrate, while the main part is reflected.The layer thickness is also an important parameter. Indeed, in orderto get a damped wave, it must penetrate a sufficient distance into theporous material. Moreover, the damping is proportional to the wavevelocity (and not the pressure) which has a maximum at a quarterwavelength away from the wall. One thus comes to the conclusionthat relatively low R s and relatively thick material should give rise tofavorable absorption properties. One should especially not think thathigh R s and small thickness give rise to good absorption. This cheapsolution leads to bad results.Frequency also plays a major role here, since the particle velocity dependson it. The friction losses, which are dependent on the viscosity,increase with increasing speed, thus increasing frequency of sound.Hence porous layers especially absorb high frequencies. Further, onemayalso imaginethatalargelayer thickness isrequired toabsorblowerfrequency (large wavelength).The pore structure also plays a role (granular or fibrous material ...).The structure can be described by means of the so-called tortuosity(this is the randomness with which the fibers are arranged in the material).The method of fixation in front of the wall. If fixed on profiles, a fewcentimeters infrontofahardwall, thenoneobtainsanabsorbenteffect,approximately equivalent to that of a layer absorbent material, equallyto the sum of the thickness of the air layer and the thickness of theabsorbent material.Caution: paint covers the fine pores and annihilates the sound-absorbingeffect of porous materials (there is no danger with large pores).Some numerical values of the specific flow resistivity : R s = 10 4 for glasswooland rockwool, R s = 10 5 for compact glasswool and compact rockwoolR s = 10 6 for compact fiberboard and R s = 10 7 for compact stony materials.∂p. ∂x

70 CHAPTER 4. SOUND ABSORPTIONFigure 4.6: Schematic of the experiment for the measurement of the specificflow resistivity.4.3 Measuring the acoustic absorptionThe acoustic absorption coefficients are material parameters that can befound from manufacturers data sheets (Table 4.1 shows the absorption coefficientsof some materials). If data sheets are not available the absorptioncoefficient must be measured as will described in this section. To measurethe absoption coefficient we will first introduce the concept of reverberationtime in the next section.4.3.1 Reverberation timeThe reverberation time T in a certain space is the time required in order thatthe energy level decreases 60 dB (which is equal to a factor 10 −6 ) :T such that I(T)I(0) = 10−6 (4.18)In what follows, we will calculate the reverberation time of a room. We willuse the following assumptions :1. The room is large : the length L 1 , the height L 2 and width L 3 ≫ λ.This means that the method is only valid for large rooms, halls, factoryhalls, etc. or smaller enclosures at higher frequencies.2. At each position on a boundary of the room, a part of the acousticenergy will be absorbed, while the remaining part is reflected.

4.3. MEASURING THE ACOUSTIC ABSORPTION 71Material 125Hz 250Hz 500Hz 1000Hz 2000Hz 4000Hzparquet flooring on concrete 0.04 0.04 0.07 0.06 0.06 0.07carpet on concrete 0.02 0.06 0.14 0.37 0.60 0.65Brick 0.03 0.03 0.03 0.04 0.05 0.07Concrete - coarse 0.36 0.44 0.31 0.29 0.39 0.25Concrete - painted 0.10 0.05 0.06 0.07 0.09 0.08Curtain 0.03 0.04 0.11 0.17 0.24 0.35Window glass 0.35 0.25 0.18 0.12 0.07 0.04Plaster 0.013 0.015 0.02 0.03 0.04 0.05Marble/tile 0.01 0.01 0.01 0.01 0.02 0.02Glasswool (5cm) 0.22 0.82 0.99 0.99 0.99 0.99Water 0.008 0.008 0.013 0.015 0.020 0.025Person 0.25 0.35 0.42 0.46 0.5 0.5Table 4.1: Absorption coefficients of some materials3. All wave propagation directions have the same probability. The shapeof the space is not of any importance, and is basically random andirregular ; however the dimensions are approximately of the same orderof magnitude.4. If a source of constant level acts in this space, a diffuse sound field willbe built up in this space after a certain amount of time. In doing so,the energy density in all points of the field will be constant.This theory neglects therefore :The direct field in the immediate vicinity of the sound source.Certainsideeffectsintheimmediatevicinityoftheabsorbingmaterials.Possible interferences and diffractions.Conclusion : In practice we assume that this theory isapplicable onlarge,possibly irregular shaped rooms, in which acoustic absorbing materials arepresent to a limited extent (the theory is not valid for an anechoic room).Consider a space with volume V, and wall surface S. Suppose that adiffuse acoustic field prevails in the space. We consider a sound source inthis space, of which the walls have a mean absorption coefficient a. Whenthe source is disabled, the intensity is I 0 . The sound dies out, i.e. theintensity will decrease due to multiple reflections and absorptions, so that

72 CHAPTER 4. SOUND ABSORPTIONafter reflection I 1 = I 0 (1 − a). After n reflections the sound intensity willbe :I n = I 0 (1−a) n (4.19)In order to determine the number of reflections n, we define :n =ct = total path length in time tmean free path(4.20)One can prove that the mean free path in a space with volume V and wallsurface S is given by 4V (without proof). Therefore we can write :SI n= (1−a) cSt cSt4V = exp ln(1−a) (4.21)I 0 4Vbecause we know x = exp(blnq) with x given by x = q b .Bydefinitionofthereverberationtimeweknowthatatt = T is InI 0= 10 −6and so :10 −6 = exp cSt ln(1−a) (4.22)4VIf we take the natural logarithm of both members of this equation, we find :T = −6.3×4×VcSln(1−a)(4.23)For air, we can obtain :T =−V6Sln(1−a)(4.24)The different walls S i of the room shall have, in practice, different absorptioncoefficients a i . We define a mean value ā of the acoustic absorptioncoefficients as : ∑ā = ∑ ia iS i(4.25)According to the model of Eyring-Norris [14], Equation 4.24 will be :i S iT =−V6 ∑ i S iln(1−ā)(4.26)We note that this model is basically valid for both small as well as largevalues of ā, but it is assumed that the absorbing materials are spatially,fairly homogeneously distributed over the walls (if not, the mean value ā hasno physically sense).

4.3. MEASURING THE ACOUSTIC ABSORPTION 73If the absorption coefficient a is small (a < 0.25) than a ≈ −ln(1 − a)and equation 4.24 :T = V6SA with A = ∑ ia i S i the total absorption (4.27)This last equation is called the model of Sabine (W.C. Sabine has found thisexpression experimentally [22]).Remark : Above theory belongs to what is called the statistical roomacoustics. It gives a certain global image of the reverberation of sound, andis based on many hypothesis and neglects many phenomena, so it does notdeliver full satisfaction to many theorists. The result is however useful andpractically well applicable.If the volume V and the reverberation time T of a space is measured, thetotal absorption can be determined with use of the law of Sabine : A = V . 6TFrom this one can determine ā SAB , the experimentally determined, averageabsorption coefficient of Sabine : ā SAB = A ∑i S i. One may thus assume, thatā SAB is a practically acceptable correct value (keeping in mind that it is aspatial and experimental average, defined by the model of Sabine). Thusin practice, the absorption coefficient shall be experimentally determined forvarious absorbing materials, making use of the model of Sabine. Would wethen estimate the reverberation time of a certain space in which absorbingmaterials are used, it can be done with the following practical model:T =V6 ∑ i S ia SAB,i(4.28)wherein the values of a SAB,i be used which can be found in tables of measurementresults. In what follows in this course, we will simplify the notationby omitting SAB, in which we however remember that each absorption coefficienta that we encounter, was determined experimentally in the mannerdescribed above.Favorablereverberationtimesdependonthetypeandusageoftherooms:for a furnished living room : 0.5 sec, for a cinema and lecture hall : 0.7-1sec, theater : 0.9-1.3 sec, music hall : 1.7-2.3 sec.In principle, one should not interpret these numbers in a too ’mathematical’manner, as having an absolute value for the acoustics of a given space.One notes, however, that the rooms which have good acoustics, have a Tthat is about within the above range. Short reverberation time gives rise to’dry sound’ i.e. sound that does not reverberate because it is immediatelyabsorbed. Several sound (e.g. music) need reverberation for their subjective

74 CHAPTER 4. SOUND ABSORPTIONappreciation. However, for speech the reverberation should not be to excessive,otherwise the syllables will overlap each other and speech intelligibilitywill be reduced. Nevertheless, the absorption can not be too big in the lattercase, because this weakens the sound pressure of the source (speaker) whichwill reach the receiver.In order to measure the reverberation time, one proceeds as follows (seealso Figure 4.7) :1. A stationary noise is produced (broadband noise, sine, etc.).2. The sound source is suddenly switched off .3. The amplitude is recorded as a function of time. The time in whicha decrease of 60 dB can be recorded, is the reverberation time T 60 .In practice, it is often not possible to lower the intensity level by 60dB because the original sound is usually less than 60 dB above thebackground noise. Instead, the time needed for a decrease of 30 dB iscalculated and the resulting time is multiplied by 2 (the measured timeis denoted by T 30 .Figure 4.7: Method for the measurement of the reverberation time.

4.3. MEASURING THE ACOUSTIC ABSORPTION 754.3.2 Measuringthe absorption in areverberation roomIf one needs to find the absorption coefficient of an object or e.g. a glasswool mattress, it is necessary to have a reverberation room at its disposal.This is a room with very hard walls (see Figure 4.8). According to theinternationalstandardsforareverberationroomV ≈ 200m 3 andV ≫ V object ,the maximum dimensions of the diagonals is 12 m, and there are no parallelsurfaces. First, the total absorption A 0 of the reverberation room itself isdeterminedduringafirstmeasurement usingtheformulaofSabine: A 0 = V6T 0in which T 0 is the reverberation time of the empty reverberation room. Next,the object is introduced and a new (shorter) value of the reverberation timeT is measured. Again follows A = V (A is the total absorption of the6Treverberation room with the object).The total absorption (room plus object) is given by A = A 0 +aS with athe absorption coefficient to be determined and S the surface of the object.Therefore :a = V ( 16S T − 1 )(4.29)T 0It suffices thus to measure two reverberation times to be able to determinea in a reverberation room. The measurement is normally carried out at anumber of normalized frequencies (i.e. band limited noise in various octavebandsisusedforthedifferent measurements ofthereverberation times). Oneshould note that a can be found in a reverberation room with the aid of apractically obtained diffuse field, i.e. for practically ’omnidirectional’ soundwaves. This omnidirectional incidence is often facilitated by hanging sounddiffusing panels (plywood or plastic) in the reverberation room.4.3.3 Measuring the absorption in the Kundt tubeMeasuring sound absorption of a material in a reverberation room is rathercomplicated because a fairly large material specimen must be available andbecause only few certified reverberation rooms are available. An alternativetest method is the so-called Kundt tube , also called impedance tube. Aschematic representation of the apparatus is given in Figure 4.9. The setupconsists of a cylindrical tube with the test specimen mounted at one end.At the other end a speaker is mounted. In the tube a rod is inserted onwhich a microphone is mounted. The the sound wave (pressure) in the tubeis measured while moving the rod through the tube. Two major parametersare recorded (these can be easily visualized on an oscilloscope) :P min the mimimum amplitude of the sound pressure

76 CHAPTER 4. SOUND ABSORPTIONFigure 4.8: Reverberation room.P max the maximum amplitude of the sound pressureThese parameters are used to calculate the so-called Standing Wave Ratio ofSWR :SWR = P maxP min(4.30)One can show that the reflection factor R (given by R = √ r, with r thereflection coefficient) can be calculated, using following equation :r = SWR−1SWR+1(4.31)From this, the absorption coefficient a can be determined : a = 1−R 2 .The method with the Kundt tube is a very simple method, which cangive fairly accurate results. There are however two major limitations in theapplication of the method :The method only gives the absorption coefficient at perpendicular incidence(in contrast to the method in the reverberation room from whicha is obtained at random incidence).

4.4. THE DIRECT AND DIFFUSE SOUND FIELD 77The measurements are only valid in a fairly limited frequency range.On the one hand there is a lower limit for the frequency f L which isdetermined by the length l of the tube : f L = 3c (at lower frequencies4Lthe minimum and maximum can not be observed within the length ofthe tube). On the other hand, there is an upper limit f U that is givenby f U = 170 with d the thickness of the tube. This limit has to bedtaken into account in order to avoid acoustic resonances in the lateraldirection of the tube. One could reduce the thickness of the tube, butthen the disturbance of the microphone on the sound field would be toolarge and the wave would be damped too much throughout the tube.Figure 4.9: The Kundt tube, used to measure the absorption coefficient of amaterial.4.4 The direct and diffuse sound fieldSuppose W is the total transmitted acoustic power of a sound source (machine)which is put in a room. In what follows, we calculate the soundpressure at a certain distance from the source.The acoustic power produced by the sound source is fully absorbed bythe walls of the room. Therefore :W = ∑ iI i a i S i = Ī ∑ ia i S i = ĪA (4.32)with Ī the spatially averaged sound intensity. For a diffuse field W = p2 effA 4ρcand thus :p 2 effp 2 0= ρcp 2 04AW 0W 0(4.33)

78 CHAPTER 4. SOUND ABSORPTIONBecause ρcW 0p 2 0≈ 1 for air, we can write :L p = L W −10logA+6dB (4.34)This way, one can determine the sound level of a given sound source ifthe absorption of the room and the sound power is known.Two different sound fields with a different propagation behavior exist :the diffuse field and the direct field. In the diffuse field the pressure is uniformthroughout the field (the propagation direction in any point is randomuniform). The diffuse field does not extend over the space, but is only validfrom a certain distance from the sound source. Close to the source a directfield is present (propagation in one direction and SPL highly dependent onthe distance to the source). For a point source in a free field the followingexpression holds (see Chapter 1) :p 2 = ρcW4πr 2 (4.35)Now, both direct and diffuse fields occur together in a space, so we haveto add the different contributions to the pressure. This is done by using theexpression for adding non-coherent sources :p 2 total = p2 direct +p2 diffuse (4.36)and thus :or in dB scale (for air) :( 1p 2 total = ρcW 4πr + 4 )2 A( 1L p = L W +10log4πr + 4 )2 A(4.37)(4.38)ThegraphofL p fordifferent valuesofthetotalabsorptonAisgiveninFigure4.10.Conclusion : at a certain distance from the source, the sound field isamplified because of the reflections which are due to the partial absorptionof the walls.The seperation between the direct free field and the diffuse field is givenby a value R of r for which both fields produce an equal sound pressure.This value R is called the reverberation radius. For the determination of thereverberation radius we write :ρcW4πR = 4ρcW2 A(4.39)

4.4. THE DIRECT AND DIFFUSE SOUND FIELD 79from which follows :R =√A16π(4.40)Within a sphere with that radius R a direct field is present, (which decreasesby 6 dB per doubling of the distance) and outside the sphere a the diffusefield is present (or reverberant field) where a constant sound level occurs,depending on the absorption A (and of course of the source power).Figure 4.10: The sound pressure level in function of the distance for differentvalues of the total absorption A.

80 CHAPTER 4. SOUND ABSORPTION

Chapter 5Sound InsulationWhen considering the sound transmission between two rooms, a distinctionmust be made between airborne sound and impact sound. In airborne sound,asource (loudspeaker, singer, radio, music instrument, aircraft, car, machine,...) generates a pressure wave in a room which is transmitted through a wallto a neighbouring room. Contact noise, on the other hand, is generatedby vibration sources (generally impacts) which leads to structural vibrationsthat propagate to neighbouring rooms (e.g. a machine fixed on the floor ora wall, footsteps, elevator).The distinction between both types of transmission is important becauseboth the transmission mechanisms, the measurement procedures and thetechniques to prevent the sound transmission are completely different. In thenext paragraphswe will focusonthesimulationandmeasurement ofairbornesound insulation (contact noise measurements will be briefly introduced).5.1 Measuring sound insulation5.1.1 Measuring airborne sound insulationIn approximation one could think of describing airborne sound insulationbetween two rooms as :∆L p = L p1 −L p2 (5.1)with L p1 en L p2 respectively the sound pressure levels in the source roomand receiving room. This would mean that the airborne sound insulation isdefined as the attenuation of airborne sound arising from the first room (representedas the difference in sound pressure level). Not only the separatingwall plays a role in the transmission of sound, but also all other boundarysurfaces of these two adjacent rooms because they can all contribute to81

82 CHAPTER 5. SOUND INSULATIONthe transmission of the sound (and vibrations) energy from one room to theother. This indirect way of transmission throughall those other boundaries /paths (other than directly through the partition which separates the rooms)is called ’flanking’ transmission (see Figure 5.1). Consequently a distinctionmustbemadebetweenthesoundinsulationRofaseparatingstructurewhichis called the ’sound reduction index’ in the international ISO140 norm, andthesoundinsulation D n between two roomswhich iscalled ’the normalizedlevel difference’ in the ISO140 norm.Figure 5.1: Flanking (2 to 4) and direct (1) transmission.It is obvious that in practice, i.e. in the acoustics of a construction,only the sound insulation D n between two rooms matters because flankingtransmission is always present. Normally we will perform the so-called ’fieldmeasurements’ of the insulation between two given rooms, where we ignorethesoundpathbetweenthesource-andreceivingroom. ThesoundinsulationD n is expressed in dB. To characterize the quality of a partition constructionby measurements all the flanking effects must be eliminated and thus a fieldmeasurement is not an option. A ’laboratory-only measurement’ must beperformed (see Figure 5.2) Such a laboratory consists of two rooms : thesource- and receiving room are independent with regard to vibrations, andthe sound transmission occurs only through the structure under test. Thisenables us to determine the sound insulation R (this is typically larger thanD n ).We will now give the formula that enables us to experimentally determinethe sound insulation as function of the frequency. Let S represent theseparation plane consisting of the wall to be tested (10 m 2 is required for

5.1. MEASURING SOUND INSULATION 83Figure 5.2: Laboratory for measuring sound insulation of a separating structure.measurements in laboratory). Because of the fact that sound transmission isa transfer of energy, we will consider the sound intensity levels :R = L I1 −L I2 = 10log I 1I 2(5.2)with I 1 the incident intensity and I 2 the transmitted intensity at the otherside of the wall. Now, the intensity level I 2 transmitted through the wallis quite difficult to measure because also the walls will contribute to themeasured sound level in the receiving room (in the normalized laboratorythe hard walls create a diffuse field). For this reason we will use the meanintensity Ī2 in the receiving room and convert this to the intensity I 2 . Bothintensities are related to each other by :I 2 S = Ī2A (the transmitted energyis absorbed by the walls with total absorption A). This means that we canwrite the sound insulation as follows :R = 10log I 1I 2= 10log p2 1because I 1 = p2 14ρcI 2 4ρcin a diffuse field.p 2 1= 10log4ρcĪ2 A Swith SI 2 = AĪ2= 10log p2 1p 2 2 A S

84 CHAPTER 5. SOUND INSULATIONand thus :R = L p1 −L p2 +10log S A(5.3)where the sound pressure level measurements are performed in tertsoctavebands (according to the international standard ISO 140). Also thetotal absorption A of the receiving room must be measured in terts-octavebands. Above equationis onlyvalid forthelaboratorymeasurement of soundinsulation of a wall (or door, window, panel, ...), whereby no flanking transmissiontakes place. The problem of the measurement of sound insulationbetween two rooms in a construction still persist. Although in this case onehas flanking transmission, it is proposed in international standard to usethe same expression (Equation 5.3) in that case, but with the surface of theseparating wall S replaced by A 0 = 10m 2 open window area :R = L p1 −L p2 +10log A 0A(5.4)Now one can compare different constructions independently of the receivingroom total absorption. The expression T is also used instead of A 0,0.5 Awith T the reverberation time of the receiving room (0.5 sec is a referencereverberation time that is typical for small rooms).5.1.2 Measurement of impact soundThe international standard ISO 140-6: 1978 describes the measurement ofimpact soundinsulationinalaboratory. Animpact device isused(see Figure5.3). It has 5 small steel hammers with normalized mass of 0.5 kg and aradius of 3 cm (the final radius is 50 cm). These hammers are aligned (0.4 mtotal length). At impact of the hammers one measure the normalized soundpressure in the receiving room :L n = L+10log A A 0(5.5)with L the A weighted SPL. Such as was the case for airborne sound insulationone measure also the standardized level (according to ISO-7 140) :L ′ nT= L+10log0.5T(5.6)

5.1. MEASURING SOUND INSULATION 85Figure 5.3: Device for measurement of impact sound insulation with fourhammers indicated by the arrows.5.1.3 Single number ratingIn the measuring procedures for acoustic insulation, described in previousparagraph (ISO 140 series), measurements are performed of the sound pressurelevels in the source-and receiving room in octave bands (or eventuallyterts- octave bands).If we want to make a statement about the insulation quality of a constructionthere is a need for a single number rating which can be compared with referencevalues. Calculation of this single number rating based on measurementsof sound insulation in octave bands is described in ISO 717-1 1982 standard.The procedure includes following steps :The measurements in octave bands or terts bands are plotted in agraph.On this same graph reference values for sound insulation are displayed(see Table 5.1.3).The reference values are shifted in steps of 3 dB until an average differenceof 1 dB with the measurements is obtained.The value at 500 Hz is recorded as single number rating (further, deviationsof more than 8 dB between the shifted reference graph and themeasurements are to be reported in addition to the value at 500Hz).

86 CHAPTER 5. SOUND INSULATIONFrequency Ref. value (in dB)100 33100 33125 36160 39200 42250 45315 48400 51500 52630 53800 541000 551250 561600 562000 562500 563150 56Table 5.1: Reference values for sound insulation of a wall from ISO 717.5.2 Airborne sound insulation of a wall5.2.1 Simple lawConsider a plane sound wave which is incident ona(simple) wall. We assumefollowing conditions are met :The wall is characterized by its mass per unit area (isotropic material).It is assumed infinitely long.The wall does not absorb sound (a = 0).The wall has no stiffness and no damping. On the source side a planeharmonic wave is normally incident on the partition wall. There is nodeformation within the wall: it displaces as a whole.On the source side one can write that the air particles have a zero velocityon the wall because this wall does not move and does not absorb sound (seealso Section 4.1). Because of the acoustically hard reflection if no absorptionis present the pressure doubles at the incident side 2p i . Applying thefundamental equation of dynamics on the wall surface :2p i −p d = ma (5.7)

5.2. AIRBORNE SOUND INSULATION OF A WALL 87with p d the sound pressure at transmission side, m the mass per m 2 and atheacceleration of this wall mass. In practice one may write 2p i = ma becausep d ≪ p i . For an harmonic wave we have p i = P i cosωt. The wall accelerationis thus a = 2 m P icosωt and his velocity :v = 2mω P isinωt (5.8)Because there is no wave phenomenon in the transverse direction in thewall it follows that v = v i = v d . The velocity v d is transmitted to the air incontact with the wall at the receiving side and gives rise to a plane travellingwave with pressure given by p d = ρcv d . It then follows that :And thus :The sound insulation is given by :and consequently :p d = ρc 2mω P isinωt = P d sinωt (5.9)P i= mωP d 2ρc = π mf (5.10)ρc∆L = 10log I iI d= 20log P iP d(5.11)∆L = 20log πmfρc(5.12)This simplified law is known as the acoustic mass-frequency law. We can seethat :By doubling the wall mass the insulation is doubled (sound reductionlevel +6 dB).By doubling the frequency the insulation is doubled (sound reductionlevel +6 dB).For a brick wall (m ≈ 100 kg/m 2 ) the application of the mass-frequency lawgives ∆L40 dB at 500 Hz.In practice the increase is smaller than what the mass-frequency law predicts:Doubling the wall mass : +5 dB.Doubling the frequency : +5 dB. (frequency-law).

88 CHAPTER 5. SOUND INSULATIONAbovemass-frequency lawwasderived assumingnormallyincident waves.One can show the following relation for sound with oblique incidence :∆L = 20logπmf cosθρc(5.13)The more oblique the incident wave, the lower the insulation value of thewall. But starting from a certain angle reflection will occur. Above model isonly valid for 0 < θ < 78 degrees. In practice sound will be incident fromdifferent directions simultaneously (e.g. in the case of a diffuse field there isa omnidirectional incidence). One can show that in this case :∆L = 20log πmfρc−5 dB (5.14)The insulation value of the wall is thus 5 dB less than for a normal incidence.For air this formula can be rewritten as :∆L = 20logmf −47.4 dB (5.15)The mass frequency law is an engineering models which attempt to give acoarse prediction of the sound insulation behavior. It does not give an exactrepresentationofthevibroacousticbehavioroftheair-wallinteraction. Inthefollowing sections we will introduce several extensions of the mass-frequencylaw.5.2.2 Effect of the wall stiffnessThe theoretical mass-frequency law showed that the mass per unit area playsan important role in sound insulation. We assumed that the wall was characterizedby its mass only and the elastic properties were ignored. If the latterproperties are considered, we notice that for the acoustic insulation propertiesthis has some negative consequences : resonance phenomena can occurat which the wall is transparant for the sound wave. This will be shown inwhat follows.Consider p − en p + the sound pressures at respectively the left and rightside of the wall, given by :p − = 2P i cosk 1 xexpiωt−iωXρ 1 c 1 expiωt+k 1 xp + = iωXρ 2 c 2 expiωt−k 2 x = P d expiωt−k 2 xThe equation of motion can now be written :mẍ+dẋ+kx = p − (0)−p + (0) (5.16)

5.2. AIRBORNE SOUND INSULATION OF A WALL 89with m the mass, k the wall stiffness and d the daming. For harmonic waveswe now that from x = Xexp(iωt) follows ẋ = iωx and ẍ = −ω 2 x. Equation5.16 can now be written in function of the amplitudes P and X (respectivelyof the sound pressure and particle displacement) :(−mω 2 +iωd+k)X = 2P i −iωρ 1 c 1 X −iωρ 2 c 2 X (5.17)or by introducing the velocity amplitude V = iωX :[i(ωm− k ω )+(d+ρ 1c 1 +ρ 2 c 2 )]V = 2P i (5.18)From the previous paragraph we know that P d = ρcV , and thus :Which gives us :P d = ρ 2 c 2 2P i [i(ωm− k ω )+(d+ρ 1c 1 +ρ 2 c 2 )] −1 (5.19)P iP d= 2(i(ωm−k) (ω d+ + ρ ) )1c 1+1 (5.20)ρ 2 c 2 ρ 2 c 2 ρ 2 c 2Three cases can now be distinguished depending on the frequency ω :1.ω ≪ ω 0 =√km⇒ R = 20logk −20logf −20log(4πρc) (5.21)For low frequencies the sound insulation of a wall is thus determinedby the wall stiffness.2.3.ω ≫ ω 0 =√km⇒ R = 20logm+20logf −20log(ρcπ ) (5.22)For high frequencies the mass of the wall is the determining factor forsound insulation (in this case the simple mass-frequency law is applicable).ω = ω 0 =√km ⇒ P ( )i d=P d ρc +2 ≈ 1 and R ≈ 0 (5.23)At the resonance frequency ω 0 the wall becomes transparant for sound.

90 CHAPTER 5. SOUND INSULATIONIt can be shown that for a rectangular wall with height a, length b andthickness h the resonance frequencies are given by [21] :f mn = π4 √ 3 c Lh(( m a )2 +( n )b )2(5.24)where the indices m and n are natural numbers designating different modesand c L the quasi-longitudinal wave velocity given by :√Ec L =(5.25)ρ s (1−ν 2 )The calculation of these frequencies allow us to estimate if the wall is eithermass controlled or stiffness controlled.5.2.3 The coincidence effectTheresonancesofthewalldescribedinpreviousparagraphoccuratrelativelylow frequencies. At higher frequencies higher order bending waves will occurin the wall (f mn for mn large). When the wavelength of these bending wavescoincides with the wavelength of the acoustic waves after projection on thewall a so-called coincidence phenomenon will occur (see Figure 5.4). Theprojection of the acoustic wavelength on the wall is called wave trace (thisis given by λasinθ with λ a the wavelength of the sound and θ the angle ofincidence). In what follows we will derive a formula for the frequencies atwhich coincidence will occur.One can show that the bending waves in a clamped wall can be describedby following equation :−B ∂4 v∂x 4 = m∂2 v∂t 2 (5.26)where B = EI1−ν 2 represents the bending stiffness of the wall (I = d 3 l/12).For an harmonic wave we have v = exp(iωt − ikx). After substitution inEquation 5.26 one gets the velocity of the bending wave :c b = √ 2πf 4 √Bm(5.27)By definition coincidence will happen when λ b = λa and thus whensinθc b = ca (because λf = c for both the acoustic wave and the bending wave).sinθThis yields :f(sinθ) 2 = c22π√ mB(5.28)

5.2. AIRBORNE SOUND INSULATION OF A WALL 91Figure 5.4: Sketch of the coincidence effect.An important frequency for the coincidence phenomenon is the so-calledcritical frequency f crit . It is the lower limit at which coincidence can occur.The critical frequency can be found by using θ = π/2 (indeed the acousticwavelength can be projected on a bigger wavelength by varying theta but noton a smaller one, θ = π/2 gives the smallest possible projection). Therefore,the critical frequency f crit is equal to :f crit = c22π√ mBFor air we can simplify this to the following expression :(5.29)√with c L =Eρ s(1−ν 2 )f crit = 64000d c L(5.30)the so-called quasi-longitudinal wave velocity of the wallmaterial. The critical frequency for somematerials isshown in Table5.2. Fora concrete wall of 10 cm thickness the value of f crit = 138.5 Hz This means

92 CHAPTER 5. SOUND INSULATIONMateriaal Densiteit E modulus c L f crit (dikte 10 mm)Aluminium 2.7 70 5367 1192Lood 11.1 16 1265 5057Beton 2.5 48 4618 1385CFRP 1.5 1.5 1054 6071Kurk 0.18 0.032 444 14400Glas 2.5 65 5374 1190Staal 7.8 210 5469 1170PU 1.2 0.025 152 42065Table 5.2: Materiaalparameters en coïncidentiefrequentie van enkele materialenthatinsulationatlowfrequencies isvery bad. Theeffect ofthislowfrequencycoincidence effect can be reduced by applying an additional material witha high critical frequency (thin material with high speed of sound) and areasonable insulation at low frequencies on the wall. An example of such amaterial is lead foil. For a thickness of 1 mm f crit = 50 kHz.The graph that summarizes the insulation behavior of a wall as a functionof the frequency is shown in Figure 5.5.5.2.4 Insulation of double wall constructionsDouble walls are used a lot in constructions. Think of double glazing, cavitywalls, ... . The main reason for their use is the high thermal insulation, butthe acoustic properties are also improved. The following practical guidelinescan be used for double walls :1. By doubling the mass the sound insulation raises with 6 dB accordingto the mass-frequency law (in reality it is only 5 dB). Appart from themass itself the air cavity also influences the sound insulation :For a distance between the walls of 2 to 4 cm the sound insulationincreases with 4 dB with respect to the mass-law.Foradistance between thewallsof5to10cmthesoundinsulationraises with 9 dB with respect to the mass-law.2. The experimental frequency law has now a slopeof 6 to 8 dB per octave(in comparison to 5 dB for the experimental law of single walls).3. In the cavity in between the double walls an acoustic resonance canoccur. This can lead to an important reduction in the sound insulationat the resonance frequencies.

5.2. AIRBORNE SOUND INSULATION OF A WALL 93Figure 5.5: Course of the insulation of a wall as function of the frequency.4. Each panel has its own resonance frequency at which its highly transmissivefor sound.5. At very low excitation both panels vibrate as a whole : eigenfrequencythe same as for single walls but with m the sum of both masses.6. The two panels form a system of two masses with a spring in between(the air layer). Let :m the mass per m 2 for each wall seperately.D the distance between both walls (=air layer thickness).P 0 the atmospheric pressure (P 0 = 10 5 N/m2)The stiffness of the spring is that of a half air layer, because the midpointstands still, if both masses vibrate with opposite phases againstthe air layer :

94 CHAPTER 5. SOUND INSULATIONk = 2×1.4P 0D(5.31)The resonance frequency is equal to :f 0 = 1√k2π m = 1√ √2.8P0 12π mD ≈ 84 mD(5.32)If the sound has a frequency equal to f 0 both walls will resonate andthus transmit the sound. For common used double glazing the insulationat low frequencies (100-300 Hz) will therefore be low (doubleglazing with m = 10 kg/m 2 and a air layer thickness of 1 cm we foundf 0 = 266 Hz).7. The air layer between the walls has also an infinite range of eigenfrequenciesat which the system becomes transmissive for sound. Thefundamental frequency is found by taking the distance d as half of thewavelength :f 1 = c λ = c(5.33)2dThe harmonics are integer multiples : f 2 = 2f 1 , f 3 = 3f 1 , ... .These frequencies are usually high. One can damp all those resonancesby applying absorbing materials between the two panels, if possible.8. Each panel has its own critical coincidence frequency. It is preferredto select the thickness of both panels different such that the criticalfrequencies do not coincide.5.2.5 Insulation of a composite wallConsider a wall with total surface S composed of different materials (e.g.windows, doors, walls, etc.) In the following we will calculate the insulationvalue of composite walls. Suppose that the wall with surface S consists oftwo components with surfaces S 1 and S 2 and that these components have adifferent insulation value :R 1 = L z −L 1 +10log S 1AR 2 = L z −L 2 +10log S 2A

5.3. THE ACOUSTICAL BARRIER 95For the complete composed wall we have :R = L z −L+10log S A(5.34)Assume that the sounds transmitted by the separate components can beadded non-coherently :It then follows that :p 2 effp 2 0= (p2 1 ) effp 2 0+ (p2 2 ) effp 2 010 0.1(Lz−R+10log S A ) = 10 0.1(Lz−R 1+10log S 1A ) +10 0.1(Lz−R+2+10log S 2A )(5.35)After elimination of 10 0.1Lz−10logA in the left– and right hand side :10 −R10 +logS = 10 −R 110 +logS 1+10 −R 210 +logS 2(5.36)The insulation R of the composite wall can be written as :R = 10log10∑i S i∑i S i10 −R i10(5.37)Example : consider a wall of 1 m × 1 m with a good insulation value(R = 60 dB). If one would make in this wall an opening of 1 mm over thewhole length, one can calculate from equation 5.37 that()1R = 10log≈0.999∗10 −6 +0.001∗10 0()1= 30 dB (5.38)0.001∗10 0This shows that the sound insulation decreases drastically is a small hole ispresent. In general the sound insulation of a composite wall is determinedby the sound insulation of the worst sub wall.5.3 The acoustical barrierOne can often see along roads – and especially highways – walls that have thepurpose to form a sound barrier of the road noise to the inhabitants living inthe neighbourhood of the road. But sound barriers are also used frequentlyin offices and factories (under the form of a screen). Part of the sound is

96 CHAPTER 5. SOUND INSULATIONblocked by the material of the screen or panel, but the sound also travelsfrom the source to the receiver in an indirect way because of diffraction (seeFigure 5.6). In order to calculate the total sound reduction one has to takethe diffraction into account. The diffraction is dependent on the wavelengthλ and thedifference d between the direct distance fromsource to receiver andthe indirect distance. The following equation gives an approximation of thesound reduction index for screens outdoors (no reflection from the ceiling) :( )λR = −10log(5.39)3λ+20dFigure 5.6 shows the graph for a frequency of 1000 Hz. Obviously onehas to be careful with these calculations. The noise level cannot be reducedmore than the surrounding noise level. The surrounding noise can also begenerated by a roadway, railway or an airport at a distance, traffic, industry,etc.In practice, in an industrial environment, one has to place the screen insuch a way that an angle of 60 degrees between the source of sound and thereceiver is obtained (see Figure 5.7).

5.3. THE ACOUSTICAL BARRIER 97Figure 5.6: Sound reduction of an infinite screen outdoors.

98 CHAPTER 5. SOUND INSULATIONFigure 5.7: Practical placement of a barrier on the work floor.

Chapter 6Noise control6.1 Origin of noiseWhen considering different sources of noise, it is useful to make a distinctionbetween the following three different types :Aerodynamic noise : the sound is generated by oscillations or frictionof air molecules in an air flow.Hydrodynamic noise : sound generated by oscillations or friction of aliquid flow.Structure-borne noise : sound generated by vibrations of a solid.Furthermore, a classification can also be made between :Active noise components : components of machines which producenoise. Usually these are the power-converting components which delivermechanical work from energy sources (electrical, mechanical ormagnetic energy, hydraulic pressure, internal forces or friction). Otheractive noise components are regions with non-stationary flow and contactsurfaces between moving parts.Passive noise components : These components conduct the noise generatedby the active components. This class can contain dominant noiseradiators, but no noise sources. Typical passive noise components arestructural components like panels.A heating system is an example of a machine with both active and passivenoise components as indicated in Figure 6.1.99

100 CHAPTER 6. NOISE CONTROLFigure 6.1: Heating system. The boiler is an active noise component and theradiators radiate the noise (they’re passive noise components).In order to consider noise control, determining the source of the noise, isthe first thing to do. Depending on the nature of this source, there are anumber of possible ways of transmission of noise and radiation of noise, asindicated in Figure 6.2.For each machine, following procedure has to be used :1. Divide the machine in active and passive noise components.2. For each component, determine whether structure-, hydrodynamic- oraerodynamic noise is generated.3. Locate the transmission paths and determine whether structural, hydrodynamicor aerodynamic noise is transmitted.4. Identify the radiating surfaces.5. Identify the primary contributions (sources, transmission paths andradiating surfaces).As an example, consider the hydraulic group in Figure 6.3. The activenoise components are : the electrical motor, the hydraulic pump and a valve.The hydraulic group has sources generating structure-borne, hydrodynamic

6.1. ORIGIN OF NOISE 101Figure 6.2: Basic model of the origin of noise in machines.and aerodynamic noise. The different types of sources and the transmissionpaths of noise are indicated in Figure 6.4.Sound power measurements are then performed on the group and theeffect of various changes is measured :1. Thepower ofsoundoftheentire aggregateismeasured (L W = 90dBA)2. The whole of motor and pump is mounted on a separate frame withvibration dampers on the reservoir. One can measure a reduced soundpower level due to the loss in transmission of structure-borne noisetransmission between the machine and the reservoir (L W = 89 dBA).3. The frame (with motor and pump) is completely decoupled from thereservoir. The connection between the pump and the valve is achievedusinga2meterlonghydraulicline. Anadditionalreductionofstructurebornenoise is realized (L W = 86 dBA).4. The reservoir is removed from the measuring chamber (L W = 86 dBA).From this, one can decide that the decoupling between pump/motorand the reservoir is sufficiently large.5. Switching to water cooling instead of air cooling with fan (L W = 85dBA).

102 CHAPTER 6. NOISE CONTROL6. The electrical motor is encased to reduce the radiated Aerodynamicnoise (L W = 81 dBA).From the measurements, a number of conclusions can be drawn :Themost importantsources arethestructure-borne andhydrodynamicnoise of the hydrostatic pump.The dominant structure-borne transmission paths were found betweenpump and motor and pump and reservoir.The dominant radiating surfaces are those of the electrical motor andthe reservoir.Figure 6.3: Hydraulic group.6.2 Reducing noise at the level of the soundsource6.2.1 Aerodynamic noise sourcesAerodynamic noise can be caused by :turbulence,vortices in the wake of obstacles in the flow,shocks and pulsations.These are discussed in the following paragraphs.

6.2. REDUCING NOISE AT THE LEVEL OF THE SOUND SOURCE103Figure 6.4: Different sources of noise and transmission paths of the hydraulicgroup.Turbulence and vorticesVortices can occur because of bodies in a flow. They generate pure tonalcomponents (e.g. the flow over a cylinder like a chimney pipe). Tonal noiseis also generated by a flow over a cavity (for example, the slicer Figure 6.5).In channels, noise can be generated by sharp corners or valves (see Figure6.6). Appart from the coherent vortical structures flow over objects can alsoresult in turbulent noise. Turbulent noise can also be produces due to shearstresses that exist when there is a gradient in the air velocity (e.g. in the caseof the the jet produced by an air gun). Turbulence gives rises to a broadbandnoise. The following design rules should be taken into account to reduce thenoise generated by turbulence and/or vortices :1. Reduce the workload2. Reduce the pressure drops3. Reduce the outlet flow rate (for example, use a larger opening ).

104 CHAPTER 6. NOISE CONTROL4. Minimize the tip speed of rotors5. Avoid obstacles in the flow or adapt the obstacles (see Figure 6.7).6. Do not point the flow outlet at the panels.7. Improve the geometry of the flow (minimize bends, narrowings). SeeFigure 6.8.8. Use special nozzles (e.g. Figure 6.9).Figure 6.5: Slicer with cavity near the blades.Shocks and pulsationsShocks are generated by a rapid discharge of a compressed medium in anarea of low pressure. This happens, for example, when opening and closinga valve in a pump. A single shock produces a broadband noise, but periodicshocks result in a tonal noise. The noise generated by this phenomenon canbe reduced by either slowing down the pressure variation or reducing thepressure difference.

6.2. REDUCING NOISE AT THE LEVEL OF THE SOUND SOURCE105Figure 6.6: Sharp corners in channels produce turbulent flow and the associatednoise production.Figure 6.7: Obstacles in the flow create flow noise.6.2.2 Sources of hydrodynamic noiseSources of hydrodynamic noise can also generate turbulence, vortices pulsationand shocks. Therefore, the design rules are the same as in previoussection.Furthermore a peculiar effect, named cavitation, can also be produced.Cavitation occurs when the static pressure is lower than the vapor pressure.Cavitation bubbles are created which implode during re-compression, so highpressures can arise. This can occur for instance invalves and pumps. Cavita-

106 CHAPTER 6. NOISE CONTROLFigure 6.8: Adjusting of the flow geometry for the reduction of the noisegenerated by turbulence.tion can be avoided by reducing the pressure drop per stage (and increasingthe number of stages). Cavitation gives rise to a broadband noise.Some design rules that are applicable for hydrodynamic noise :1. Reduce the pressure drop2. Reduce the flow rate3. Increase the static operating pressure4. Improve the geometry to counter cavitation5. Keep the suction ducts short

6.2. REDUCING NOISE AT THE LEVEL OF THE SOUND SOURCE107Figure 6.9: Use of special composed silent nozzles.6. Position the reservoir higher than the inlet of the pumpFigure 6.10: Cavitation and solution to the cavitation phenomenon.

108 CHAPTER 6. NOISE CONTROL6.2.3 Sources of structure-borne noiseImpact noiseImpact noise is one of the most dominant noise sources in many machines.The most important parameters of impact noise are the mass and velocity ofthe impact bodies and the duration of the impact. The frequency spectrumof one single impact shows that this is a broadband noise. Repeated impactsgenerate also harmonic noise.Some practical design rules for the reduction of impact noise are :1. Increase the time of the impact,2. Decrease the speed of the impact (see e.g. in Figure 6.11),3. Minimize the mass of the impact body,4. Increase the mass of the solid body,5. Avoid loose parts with varying load.Figure 6.11: Reduce the impact speed of a conveyor belt.GearingThis is a special form of impact noise that occurs e.g. in gearboxes. Importantparameters are the contact period, the time variation of the force duringcontact and the stiffness of the teeth. Defects in the teeth may cause extraforce variations and thus more noise. A tonal noise is produced (with tonesat multiples of the tooth frequencies).Measures to reduce the generated gearing noise are :

6.2. REDUCING NOISE AT THE LEVEL OF THE SOUND SOURCE1091. Increase the contact time2. Use helicoidal gears3. Increase the number of teeth4. Improve the quality of the transmission (alignment, accuracy of thegearing),5. Use plastic gears for small loadsRolling noiseRolling noise is the result of the roughness or the irregularity of the contactsurfaces. Rolling noise occurs in roller and ball bearings, belts, rail androad vehicles. The rolling noise also depends on the flexibility of the contactsurfaces. The frequency content of rolling noise is mainly broadband.The design rules for rolling noise are :1. Provide a smooth roll surface2. Use suitable lubrication3. Use precision bearings4. Minimize the tolerances of the housing of the bearings5. Increase the flexibility of the contact areaInertiaAcceleration of a mass leads to forces that can produce noise e.g. by impact,rolling, friction or pulsation. Inertia forces can be caused by oscillatingmasses or by (non-balanced) rotating parts.Inorder tocontrol inertia noise, onehasto takeinto account the followingdesign rules :1. Balance rotors or use dynamic balancing2. Minimize accelerating masses3. Increase the uniformity of motion

110 CHAPTER 6. NOISE CONTROLFrictionMechanisms where friction causes a so-called stick-slip phenomenon, are potentialnoise sources. The variation of force leads to impact noise that canexcite the resonances of the structure. Friction noise occurs e.g. in brakediscs. The phenomenon is dependent on the materials and lubrication. Inprinciple, friction noise is broadband, but often due to the resonances strongtonal components can occur.Some design rules :1. Control friction by suitable selection of materials2. Use suitable lubrication3. Increase the damping of the structure6.3 Tackling noise transmission6.3.1 Transmission of aerodynamic noiseAerodynamic noise generated in parts of the machine is passed to the surroundingsby the air (one speaks of air-borne noise). There are several waysto control this transfer :Acoustic casing. Usually made of a metal plate. Absorption materialcan be placed on the inside to reduce the noise production. Someconsiderations :1. The casing must be completely sealed (even small holes andcracksshould be closed).2. Use heavy materials for the outer wall (see mass-frequency law toevaluate the acoustic insulation).3. Use absorbing materials for the inside.4. Use dampers for openings (ventilation, cables).5. Avoid rigid connections with the machine (as few as possible connectionpointswithvibrationdamping). Use aflexible connection,optionally with damping (see Figure 6.12).6. Sometimes enclosing the different parts can be effective.Acoustic screens. Screens can be installed near to parts with largeemission of noise. However their efficiency is much lower than casings

6.3. TACKLING NOISE TRANSMISSION 111and depending on the direction and the distance. The shielding of themachine by means of a cap only has an effective noise damping effectif:– It is composed of sufficiently heavy material– The cap on the inside is coated with noise absorbing material– The openings are limited to a minimum– The cap is isolated from the machine and/or is made of/or coatedwith an already resilient material (wood instead of steel plate,steel sheet coated with rubber, ...).Noise Mufflers. Noise dampers are parts tthat counter the transmissionof Aerodynamic noise through openings. Absorption Mufflers(Figure 6.13) consist of a channel (or a system of channels) filled witha porous material. Another type is the reflection muffler (Figure 6.14)that muffles the noise by the reflection of noise at a change of thecross-sectional area (in this case, the impedance also changes). Someguidelines for the use of mufflers :1. Useabsorptionmufflersforbroadbandnoiseandreflectionmufflersfor low-frequency noise.2. Avoid speeds bigger than 20 m/s in an absorption muffler.3. Use pneumatic expansion mufflers for the exhaust of compressedair.Noise absorption.Figure 6.12: Flexible connection with the machine.

112 CHAPTER 6. NOISE CONTROLFigure 6.13: Absorption muffler.Figure6.14: Reflectionmuffler. Above: differentpossiblereflections. Under:reflection muffler in an exhaust system.6.3.2 Hydrodynamic noise transmissionTransmission of hydrodynamic noise takes place in pipes and tubes. Noisecontrol can be done at the inlet of the system, in the system or at theoutlet. The means is both reflection and absorption. Reflection is obtained

6.3. TACKLING NOISE TRANSMISSION 113at the end of the system due to changes in the cross-sectional area or bychanging the rigidity of the wall by transition of pipes to tubes. Absorptionof Hydrodynamic noise is provided by accumulators. The design rules forthe control of liquid-born noise are :1. Use a combination of pipes and tubes.2. Use dampers.6.3.3 Structure-borne noise transmissionThe transmission of structure-borne noise from sources to radiating surfacescan be influenced by changing the mass, stiffness and damping of the structure.The selected strategy depends on a number of factors :Is an increase of weight possible or not? If so, an increase of mass nearthe region of excitation will be efficient.Force excitation or speed excitation? In case of force excitation, addingimpedance (mass) will be effective, in case of speed excitation, addingmass has no sense (in the latter case, the source may be isolated).Narrow-band or broadband excitation? For a narrow-band excitation,it is advisable to redistribute the stiffness or mass of the system (inorder to shift the resonance frequencies). The addition of damping canalso be effective. This has no sense for broadband excitation and abroadband reduction of the transmission needs to be obtained.Excitation at low frequencies, intermediate frequencies or high frequencies(quasi-static, resonance or multi-resonance response respectively)?At low frequencies, vibration isolation is the only possible solution.Panels with free edges radiate, in general, less noise than clamped panels(see Figure 6.15). In the middle frequency region, a number ofsolutions can be chosen :– Adding mass at the excitation point (see Figure 6.16).– Increasing the structural damping– Isolate the source (e.g. see Figure 6.18).– Reflection at discontinuities (see Figure 6.17).In the high frequency region, the following measures can be effective :– Increasing the mass or stiffness of the excitation region.

114 CHAPTER 6. NOISE CONTROL– Isolation of the source.– Discontinuities in combination with extra damping.Increasing only the damping is not sufficient in this area.Figure6.15: The cart with freepanels emits less sound thanthe original cart.Figure 6.16: Lowering the transmission by increasing the mass.

6.4. RADIATION NOISE 115Figure 6.17: Reduction of the transmission of structure-borne noise by discontinuities.Figure 6.18: Isolation of structural noise in pipes.6.4 Radiation noiseAir-borne noise can be radiated through outlet openings (e.g. the end of atube). Usually the noise has a directivity in the direction along the axis ofthe tube. The opening can be adjusted to reduce the noise in this direction.

116 CHAPTER 6. NOISE CONTROLThe design rules are in this case :1. Put the openings in the right place and point them in the right direction.2. Use a damper or screen at the opening.Structure-borne noise radiation depends on the size, shape, flexibility,mass and damping. Regarding radiation, it is desirable to design the areaswhich are loaded, as compact as possible. Design rules for structure-bornenoise radiation :1. Reduce the radiation surface (see Figure 6.19).2. Use lids with low radiation efficiency :Thin plates instead of thick plates.Perforated plates (see e.g. Figure 6.20).Panels with damping material (bitumen, constrained layer dampingmaterial), see Figure 6.21.Figure 6.19: Reducing the radiation surface.

6.4. RADIATION NOISE 117Figure 6.20: Casing of a belt drive with a perforated panel.Figure 6.21: Damping of panels.

118 CHAPTER 6. NOISE CONTROL

Part IIINoise directives119

Legislation concerning sound is highly complex matter. There is legislationon various level that often contradicts :Community level (e.g. police regulations).121Regional level (e.g. in Flanders there exists the Vlarem II for communitynuisance).National level (legislation for noise exposure for workers).At the international level (European).Often thescope of applicationis not clear andthe guidelines, noise indicatorsand norms can contradict.In the past few years more and more local legislation is replaced by Europeanregulations. The motivation for this is bipartite :Economical : promote the free traffic of goods in between EU membersstates.Social : protect the EU citizens.In this course we will concentrate on three European noise guidelines :The directive concerning machines in open air.The directive on exposure of workers in industry.The directive for environmental noise.Remark that the directives that are discusses are no laws. Each of themhas to be converted into national legislation by national governments. Thedirective becomes a law from the moment it is published in the national stategazette after conversion.The European guidelines can be downloaded (without charge) from thewebsite http://europa.eu.int. The conversion of the European regulations inthe Belgian legislation can be accessed via the state gazette, where the documentsareavailabledigitally(website:http://www.ejustice.just.fgov.be/cgi/welcome.pl).

122

Chapter 7Directive 2000/14/EG :’Machines in open air’In may 2000, the guideline (also called directive) ’on the harmonisation ofthe legislations of the member states concerning the noise emission in theenvironment by equipment for outdoor use’ (2000/14/EG) was published.This guideline was converted in a Belgian national law on the 6 th of March2002 and was published in the Belgian state gazette on the 12 th of March2002 (from that moment on it is applicable).The goals of this guideline is the standardization and uniformization ofthe legislations of the member states concerning noise emission standards,assessment procedures, marketing, technical documentation and collection ofdata concerning noise emission in the environment by equipment for outdooruse. The guideline will contribute to the proper functioning of the marketwhile at the same time it is beneficial to the human health and well being.Therefore, this guideline is in first instance an economical guideline.The guideline concerns all machines for outdoor use that are put out onthe market after 1/1/2002. The guideline applies to the manufacturers ofmachines and it does not aim at the users of equipment. Depending on theirtype, all machines are divided in two groups that are listed explicitly in theguideline :The machines that are listed in Article 12 of the guideline. For thesemachines, limit valuesfortheproducedguaranteedsoundpowerlevelsL WA are given in the directive. Examples : compressors, dozers, excavationmachines, welding generators, lawnmowers, current generators,etc.The machines listed in Article 13 of the guideline. For these machinesNO limit values for the sound power level are applicable. Examples :123

124CHAPTER 7. DIRECTIVE 2000/14/EG: ’MACHINES INOPEN AIR’chainsaws, pressure washers, leaf blowers, concrete mixers, choppers,etc.with guaranteed sound power level meaning : the measured sound powerlevel including the uncertainties due to the variations in the production andthe measuring methods.A detailed description of all machines and specific measurement methodsfor the sound power is given in Appendix 1 of the guideline. The guidelineonly concerns equipment that is put on the market or is used as a whole.Non powered parts that are put on the market, or are being used separately,are not considered in the directive.The guideline is not applicable to :Equipment that is primarily used for the transport of goods or personsover the road, by railway, by air or over water.Equipment for military or police use or for emergency services.For machines named in Article 12, a list is included in the guidelines withacceptable sound power levels. (an extract from this list can be found inFigure 7.1). In function of the power of the machine a different acceptablelevel is defined. Next to limits on the produced sound power there are a fewother measures that must be taken for machines in Article 12 :Assessment procedures before bringing the product on the market.CE marking of the product with guaranteed L w (see Figure 7.2).A written EG-declaration of conformity must be available.Technical documentation (with measurements) must be available.The documentation should be assessed by by a certified body (companieslike Vincotte, SGS, etc.).Periodicalproductioninspectionsshouldbeperformedbycertifiedbodies.The EG-declaration of conformity must contain the following data:Nameandaddressofthemanufacturer orhisauthorizedrepresentative.Name and address of the person who stores the technical documentation.Detailed description of the equipment.

125Followed conformity assessment procedures and optionally the nameand address of the involved certifying body.Measured sound power level of a machine that is representative for thistype of equipment.Guaranteed sound power level of the equipment.A reference to the EU 2000/14/EG guideline.A declaration that this equipment is conform the prescriptions of theguideline.If applicable, the declaration(s) of conformity and references to othercommunity guidelines that are applied.Place and data of the declaration.Name, address and date of birth of the person who is authorized to signthe declaration for the manufacturer or his authorized representative.For the machines listed in Article 13, the first four measures are the sameas for those in Article 12. The last two requirements are less strict however :The assessment of the technical documentation may be done by themanufacturer of the machine.The manufacturer can inspect the production himself.Figure 7.1: Example of the acceptable sound power levels as described inappendix 1 of the guideline 2000/14/EG.

126CHAPTER 7. DIRECTIVE 2000/14/EG: ’MACHINES INOPEN AIR’Figure 7.2: Example of a CE label with the guaranteed sound power level.

Chapter 8Noise on the work floorDeafness due to exposure to noise on the work floor is the most commonoccupational diseases in the EU. The Belgian national Fund for occupationaldiseases publishes every year statistics with different causes of occupationaldiseases. FromthegraphinFigure8.1itcanbeseenthatinBelgiumdeafnesstook place number 1 in the causes of permanent unfitness for work.To reduce the risk of exposure to noise, the EU has introduces a newguideline on exposure of workers to noise in the nineteen eighties. On the12 th of May, 1986 the EEG guideline 86/188/EEG concerning protection ofemployees against the risks of exposure to noise on the work floor was issued.It isclearfromFigure8.1thattheintroductionofamorestringent regulationlead to an important reduction of the number of cases of deafness in the latenineties. This 86/188/EEGdirective will be discussed in the next paragraph.Because it became clear that the acceptable noise levels in industry wouldnot lead to a further decrease of the number of deaf worker a new directivewas prepared in the early nineteen nineties. After more than ten years thishas lead to the EU guideline 2003/10/EG that is applicable at this moment.In general the permissible noise levels on the work floor in the 2003/10/EGdirective arelower than before. The new directive will be discusses in Section8.2.8.1 Previous guidelineThe guideline 86/188/EEG is accepted and took effect in Belgium throughthe royal decree of 26.09.1991 (see Belgian state gazette of 14.11.1991). Thegoal is to protect all employees against the hazards coming from exposure tonoise, for their hearing, health and safety. The guideline aims at reducingthe risks of exposure to a minimum level, taking into account the technical127

128 CHAPTER 8. NOISE ON THE WORK FLOORFigure 8.1: List of the causes of permanent unfitness for work in the past 20years. Source : Fund for occupational diseases.development and the protection of measures to control the sound at thesource. When the exposure probably exceeds 85 dBA;The employer must provide means to protect the hearing to his employeesin a sufficient degree;Exposed employees have the right to have a hearing examination.The employees (or their representative in the enterprise) receive anadequate information session or possibly education towards the risks ofexposure to noise.When the daily exposure exceeds 90 dBA the following obligations mustbe fulfilled :The causes of the noise must be identified and a program for the reductionof the noise must be set up.

8.2. PRESENT GUIDELINE: DIRECTIVE 2003/10/EG 129The work place must be indicated with appropriate signalization.Individual hearing protection must be used.Although this legislation is more strict than the older national regulation,the admissible exposure levels are still much higher than the lower limitwhere, at long exposure hearing impairment will occur (this threshold is 80dB). Because of this a new European regulation was introduced with loweraction values : guideline 2003/10/EG.8.2 Present guideline: directive 2003/10/EGThe European guideline 2003/10/EGConcerning the minimum prescriptionson health and safety with regard to the exposure of employees to risks ofphysical agents (noise) was converted into a national legislation on the 16 thof January 2006 (BS 15.02.2006).The law is applicable to employers and employees and includes all activitieswhere employees can be exposed to risks related to noise on theirwork.Two exposure levels that are used as action- and limit values are definedin the legislation :(Daily exposure to noise) (L EX,8h ) (dB(A) re. 20 µPa) : this is thetime weighted average of the levels of exposure to noise on a normalwork day of 8 hours.L EX,8h = L Aeq,Te +10log T eT 0(8.1)whereL Aeq,Te = 10logand T 0 = 28800 seconds.(1T e∫ Te0(pA (t)p 0) 2)(8.2)Weekly exposure to noise (L EX,8h ) : the time weighted average of thedaily levels of exposure to noise in an normal week of five working daysof 8 hours. ( )L w EX,8h = 10log 1m∑10 0.1(L EX,8h) k(8.3)5k=1Three important values are fixed in the legislation :

130 CHAPTER 8. NOISE ON THE WORK FLOORVoice normal loud very loud shouting extremeLevel (dBA) 50 70 85 90 100satisfaction + ± - - - - - -Risk slight nuissant small risk average risk important riskinconvenience of deafness of deafness of deafnessTable 8.1: Qualitative assessment of the noise level on the work floor.The lower action value : L EX,8h = 80dBA or a peak value of 112 Pa.The upper action value : L EX,8h = 85dBA or a peak value of 140 Pa.The limit value : L EX,8h = 87dBA or a peak value of 200 Pa. Thisvalue may not be exceeded under any circumstances. Attention : thisvalue must be measured taking into account to the damping of themeans of hearing protection. This is different from the work methodin the previous guideline where hearing protection was not taken intoaccount.In the context of the risk analysis and based onthe formulated preventionmeasures, the employer examines if employees canbe exposed to risks relatedtonoiseduringtheirwork. Ifitisshownthatemployees canbeorareexposedto risks related to noise, the employer assesses and if necessary measures thelevel of exposure of the employees to this noise (the employer can potentiallyattract an internal or external prevention advisor to do this). The employerchecks if the action and limit values are exceeded. A qualitative estimationof the noise levels can be performed in a simply but effective way: one has aconversation over a distance of one meter between source and receiver. Thedegree with which the voice must be raised gives an indication of the soundlevel (see Table 8.1).When the upper action values are exceeded, the employer proceeds to theforming and execution of a program of technical and organizational measuresto limit the exposure to noise to a minimum. A few possibilities that aredescribed in the legislation :1. Alternative working methods that lead to less exposure to noise.2. The choice of the appropriate tools, with regard to the work that needsto be performed in order to produce the least noise as possible.3. An adequate prevention and education of the employees to teach themhow to use tools correctly in order to limit the exposure to noise to aminimum.

8.2. PRESENT GUIDELINE: DIRECTIVE 2003/10/EG 1314. Technical measures to limit noise are taken :(a) Pursuant air noise, especially by shielding, enclosure or coveringwith sound absorbing material;(b) Pursuant construction noise, especially damping or insulation;5. Appropriate maintenance programs for work equipment, the shop floorand the systems on the shop floor;6. The organisation of work, in view of limiting the noise :(a) Restriction on the duration and intensity of the exposure;(b) Custom work schedules and a sufficient amount of breaks.Moreover, the zone where the upper action value is exceeded is indicatedwith custom signalisation (see Figure 8.2).In no circumstances the exposure of the employee may exceed the limitvalue. If, notwithstanding all precautions that were taken, it is shown thatthe exposure exceeds the limit value, the employer must :1. Immediately take action to reduce the exposure to a level below thelimit value for the exposure.2. Determine the cause of the exceeded exposure3. Adjust the protection- and prevention actions to prevent the problemfrom occurring again.Figure 8.2: Indication of the zone where the upper action value is exceeded.

132 CHAPTER 8. NOISE ON THE WORK FLOORIf risks arising from the exposure to noise cannot be prevented in anyother way, appropriate, properly fitting individual hearing protection mustbe made available to the employees :When the lower action value is exceeded, hearing protection is madeavailable for the employees.When the upper action value is exceeded, hearing protection must beused.The individual hearing protection is selected in such a way that the risk onhearing impairment is eliminated or limited to a minimum (see further). Theemployer is responsible for the application of the actions taken in this articleand takes care that the employees wear the hearing protection.The employees thatexecute anactivity witharisk duetonoise, where theexposure exceeds the lower action value, are subject to prior health examination(an examination of the hearing by means of a pre-emptive audiometricexamination, see further). The periodicity of the health examination is determinedas follows :Yearly for employees who are exposed to a daily average exposureequal or larger to 87 dB(A) or a peak sound pressure of 140 dBC;Once every three years for employees who are exposed to an averagedaily exposure equal to or larger than 85 dB(A) or a peak soundpressure of 137 dBC;Once every five years for employees who are exposed to an averagedaily exposure equal or larger than 80 dB(A) or a peak sound pressureof 135 dBC.8.3 Risk of hearing damageOccupational deafness is permanent and irreversible hearing loss, caused byordinary working conditions. Certain types of occupational deafness maybe due to toxic products such as carbon monoxide (CO), carbon disulfide,benzene and lead. Others are due to brief exposure to intense sounds (e.g.gunshots or explosions), wherein a rupture occurs of the basilar membranein the cochlea of the eardrum, or, in the case of an explosion, the ossicles areaffected.

8.3. RISK OF HEARING DAMAGE 133In what follows we will consider occupational deafness due to noise. Thiskind of deafness is bilateral (both ears) and usually symmetrical. It’s irreversibleand does not evolve if there is no exposure to noise anymore. Occupationdeafness evolves according to the duration of exposure. First there isa slight loss between 3 and 6 kHz, generally at 4 kHz. If exposure to noisepersists, the loss will get larger around the initial frequency : the loss canamount to 20 to 40 dB, but is not observed by the employee because thespeech frequencies are involved to a lesser extent. Then the loss becomeslarger at low frequencies : the person starts to encounter difficulties in conversationsin a noisy background or to use the phone. Finally, the loss canprogress to severe deafness, making each auditory communication difficult oreven impossible.The risk of hearing loss can be calculated from the data in the internationalstandard ISO1999:1990. Auditory data of employees which wereexposed for a long time to noise at the work floor, are processed in this standard.An extract of the standard is given in Figure 8.3. From this standardappears clearly that the former directive, where a limit of 90 dBA was used,still entailed a significant risk of hearing damage (20% risk at 35 years ofexposure).Figure 8.3: Data from the ISO1999 standard in which the risk of hearingdamage is indicated in function of the level of exposure (different graphs)and the number of years of exposure (x-axis).

134 CHAPTER 8. NOISE ON THE WORK FLOORA loss of auditory functions can lead to:A social disability, when the person has difficulties to have a conversations.Incapacity for work: if he is unfit to continue working.Invalidity, if the suffered physiological loss is too large.It is important to make a distinction between these three concepts and, inparticular, between the last two : incapacity for work is a relative concept,while invalidity is assessed as absolute. Hereafter we will only focus on thecriteria for social disability and invalidity. The question arises which frequenciesshould be used to measure disability or invalidity? Since the speechfrequencies are located between 250 or 4000 Hz, it would be logical to definethe average hearing deficiency as the average of the loss at the octave bandfrequencies 500, 1000 and 2000 Hz. The most widely accepted scale w.r.t.hearing disability which is based on that average, is that of the AmericanAcademy of Ophtalmology and Otolaryngology:disability = 1.25D b +0.25D m −39 (8.4)with D b and d m the hearing loss in the best ear and the average hearingloss of the weakest ear respectively. So the disability is 0 if D b or D m < 26dB. Disability would therefore occur starting from a loss of 26 dB and wouldreach 100% (full deafness) for a bilateral loss of 93 dB. In the calculation ofthe average hearing loss is currently the loss at 500 Hz replaced by that at3000 Hz. It has been attempted to justify this change by underlining that itis not only the person’s ability to hear, but also to understand the words insound conditions that correspond to those of everyday life and not just in acalmenvironment, whichisimportant. Thefrequency of3kHzisincreasinglyimportant as the rate of speech increases and as the the distortion due tothe background environment increases. Based on these frequencies one candefine the disability rate as :Disability = 1.25D b +0.25D m −39 (8.5)so the disability is 0 if D b or if D m < 35 dB. The handicap threshold shouldtherefore be increased to 35 dB as the hearing loss is calculated based on thefrequencies 1, 2 and 3 kHz. The Fund for Occupational Diseases in Belgiumhas decided to choose the losses at 1, 2 and 3 kHz for the calculation of theaverage loss. The scale for physical incapacity for work is the following :50 to 55 dBA : 1 to 5 % incapacity for work

8.4. THE AUDIOMETRIC EXAMINATION 13555 to 65 dBA : 5 to 10 % incapacity for work65 to 75 dBA : 10 to 30 % incapacity for work75 to 85 dBA : 30 to 55 % incapacity for work75 to 100 dBA : 55 to 80 % incapacity for workNote that a person can never be 100% incapable for work by deafness. Aperson who in fact is socially affected by the sustained deafness, is thereforenot incapacitated (threshold of 50 dBA compared to 35 dBA for disability).8.4 The audiometric examinationThe audiogram is an objective measure of hearing loss or deafness. It is thegraphic representation of the hearing loss relative to the reference measuredwith an audiometer. In this context, one speaks of the Bekesy audiometry.This is a type of automatic tone audiometry. There is also speech audiometry.This is done by testing speech intelligibility of one-syllable words, theso-called PB-lists (PB stands for phonetically balanced). In the Bekesy audiometry,a device is used that automatically passes 7 test tones (500, 1000,2000, 3000, 4000, 6000 and 8000 Hz) and this for both ears separately. Thesubject presses a button when he hears the tone, he releases the button whenhe does not hear any sound. After the button has been pressed, the intensitydecreases gradually. After the subject releases the button, the intensity increases.This results in saw-tooth-shaped curve of the sound levels at whichthe respondent reacted. For standardization, the device must be calibratedon a so-called artificial ear. Audiograms of the automatic method can berecorded with a pulsating sound or a continuous sound. The pulsating soundis typically 260 ms on and 260 ms off. Tone audiometry learns us a lot aboutthenatureofthehearingloss. Inaudiometry, aboneconductionaudiogramisoften used as an additional diagnosis. A vibrating plate mounted directly onthe skull is used instead of a loudspeaker (in the case of the air-transmissionaudiogram). The vibration propagates through the head until it reaches thecochlea. Some examples of audiograms are shown in Figure 8.4.A number of diagnoses can be made from audiograms :1. If the bone conduction audiogram is normal and the air conduction audiogramshows a significant loss, then the problem is probably situatedin the ear canal or in the middle ear. With such an audiogram, thepatient would, for example, suffer of otitis (ear infection).

136 CHAPTER 8. NOISE ON THE WORK FLOOR2. If there is only low frequency loss, this indicates a malfunction of theossicles. This may be a consequence of otosclerosis.3. A ’notch’ in the audiogram at higher frequencies is the beginning stageof perception hearing loss and is usually a result of noise exposure.4. Furthermore, one can also compare two audiograms that were obtainedwithpulsed tones andcontinuous tones. The sensitivity to pulsed tonesappears to be higher than to continuous tones. This is called pathologicaladaptation or ’tone-decay’ : a tone, initially heard, disappears.When the variation between both audiograms is larger than 20 dB, it isassumed that the condition is part of retro-cochlear nature. If the continuousdiagram lies above the pulsating diagram, then this is probablya sign that the subject attempts to simulate deafness.Figure 8.4: Example of an audiogram of a normal hearing person and twohearing-impaired persons. Source: www.kennislink.nl

8.4. THE AUDIOMETRIC EXAMINATION 137sound level (in dBA) 85 87.5 90 92.5 95 97.5 100% time (in %) 0% 44% 68% 82% 90% 96% %97Table 8.2: Percentge of time of which the PPE must be worn to reduce theexposure level to 85 dBA.8.4.1 Personal hearing protectionWhen the risk of exposure to noise can not be reduced by technical or organizationalmeasure, personal protective equipment (PPE) is made availableto reduce risk. There is a very wide range of PPEs, which are divided intofour groups (see Figure 8.5) :The earmuff (attenuation 15 to 30 dBA),The earplug (attenuation 15 to 25 dBA),The ear gag (attenuation 10 to 15 dBA),The ear clip (attenuation 10 to 15 dBA).Although the attenuation of the PPE is more important, it seems in practice,that comfort and covenience prevail. Indeed, if the comfort is not optimal,workers will not wear the PPEs during the whole exposure time. Table 8.2shows that at a sound pressure level of 95 dBA, the PPE needs to be wornduring 90% of the time in order to be effective (even if the attenuation isvery high).Besides the comfort and convenience, there are a number of other parametersin the selection of PPEs :Environmental conditionsNature of work (free space)Duration of exposureNecessity to wearMedical problemsCE certification (see directive EG 89/686)Need of ability to communicateCompatibility with other protective equipment

138 CHAPTER 8. NOISE ON THE WORK FLOOR(a)(b)(c)(d)Figure 8.5: Personal hearing protection.

Chapter 9Community noiseUnder community noise (also called environmental noise, residential noise ordomestic noise) we understand outdoor noise emitted from human activitiesincluding road traffic, rail traffic, air traffic and locations of industrial activities.In this chapter the legislation concerning community noise will bediscussed. In 2002 a new EC directive for community noise was published :2002/49/EC guideline. The aim of this directive is to commit EU MemberStates to register and reduce environmental noise. The Member States areresponsible for the follow up of the legislation (the directive has therefore atpresent no direct consequences for companies).9.1 EC directive 2002/49/ECNoise is one of the most important environmental problems in Europe. However,there is a lack of reliable data to determine noise in the different EUmember states. Data from the different states exist but due to the use ofdifferent indicators a comparison between sources of noise is not possible.The EC directive 2002/49/EC ’ relating to the assessment and managementof environmental noise’ has te following purposes:1. The harmonization of noise indicators and assessment methods. Forthis purpose two indicators were introduced which have to be used byeach of the EU member states :L den = 10log 124(12∗10 −L day10 +4∗10 −L evening +510 +8∗10 −L night +1010(9.1)whereby L day , L evening and L night are the equivalent sound pressurelevels measured during the day, evening and night. L den is used toasses annoyance and L night to asses sleep disturbance.139)

140 CHAPTER 9. COMMUNITY NOISE2. Noise mapping (see Figure 9.1 where the noise mapping of Netherlandis shown).3. Making action plans to reduce the environmental noise.4. To make this information accessible for public.Figure 9.1: Noise map of Netherlands. Bron:http://www.milieuennatuurcompendium.nlThe realization of the directive by the EU member states should happenin two phases :1. By30June2007allagglomerationswithmorethan250.000inhabitantsand all road traffic with more than 6 million vehicles/year, rail trafficwith more than 60.000 trains/year and airports with more than 50.000movements/year have to be measured (L DEN ) and noise maps have tobe made.

9.1. EC DIRECTIVE 2002/49/EC 1412. By 30 June 2012 noise maps of all agglomerations (with more than100.000 inhabitants), as well as road traffic with minimum 3 milionvehicles/year, rail traffic with more tha 30 000 trains/year and airportswith minimum 50 000 movements/year should be available.The next step in the directive is an information campaign for the publicabout environmental noise and the effects. Finally, action plans are to bemade by the EU member states to avoid and limit environmental noise :1. By18July2008: largeagglomerations(morethan250.000inhabitants).2. By 18 July 2013: all agglomerations (more than 100.000 inhabitants).

142 CHAPTER 9. COMMUNITY NOISE

Appendix AMaterial properties143

144 APPENDIX A. MATERIAL PROPERTIESTable A.1: Properties of gasses, liquids and solids, Source : [6]

145

146 APPENDIX A. MATERIAL PROPERTIESTable A.2: Mechanical properties of solids, Source : [6]

Table A.3: Absorption coefficients.147

148 APPENDIX A. MATERIAL PROPERTIES

149

150 APPENDIX A. MATERIAL PROPERTIES

Bibliography[1] ISO 3741. Acousticsdetermination of sound power levels of noisesourcesdiscrete- frequency and narrow-band sources in reverberationrooms. InternationalOrganizationforStandardization, Geneva, Switzerland,1986.[2] ISO 3742. Acousticsdetermination of sound power levels of noisesourcesdiscrete- frequency and narrow-band sources in reverberationrooms. InternationalOrganizationforStandardization, Geneva, Switzerland,1986.[3] ISO 3743. Acousticsdetermination of sound power levels of noisesourcesspecial reverberation test rooms. International Organization forStandardization, Geneva, Switzerland, 1986.[4] ISO 3745. Acousticsdetermination of sound power levels of noise sourcesanechoic and semi-anechoic rooms. International Organization for Standardization,Geneva, Switzerland, 1986.[5] ISO3746. Acousticsdetermination of sound power levelsof noisesourcessurveymethod. International Organization for Standardization, Geneva,Switzerland, 1986.[6] R. Barron. Industrial Noise Control and Acoustics. Marcel Dekker, NewYork, 2003.[7] Beranek. Noise and vibration control. Mc Graw-Hill Book Company,New York, 1971.[8] Beranek. Acoustics. Acoustical Society of America, New York, 1996.[9] L. L. Beranek. Noise Reduction. McGraw-Hill, New York, 1960.[10] Bruel and Kjaer. Het meten van geluid. 1985.[11] Bruel and Kjaer. Sound level and frequency of sound. 1985.151

152 BIBLIOGRAPHY[12] Bruel and Kjaer. Noise control. Danmark, 1986.[13] Cremer and Heckl. Structure borne sound. Springer-Verlag, Berlin,Germany, 1988.[14] C.F. Eyring. Reverberation time in dead rooms. J. Acoust. Soc. Am.,1:217–241, 1930.[15] H. Fletcher and W.A. Munson. Loudness, its definition, measurementand calculation. J. Acoust. Soc. Am., 5(2):82–105, 1933.[16] Harris. Handbook of noise control. Mc Graw-Hill Book Company, NewYork, 1979.[17] ISO/TR11688-1:1991. Acoustics - Recommended practice for the designof low-noise machinery and equipment. ISO, Switserland, 1995.[18] Lyon. Machinery noise and Diagnostics. Buttersworths, Boston, USA,1987.[19] A.D. Pierce. Acoustics: An Introduction to Its Physical Principles andApplications. McGraw-Hill, New York, 1981.[20] J.W.S. Rayleigh. The Theory of Sound. Dover Publications, New York,1945.[21] R. J. Roark. Formulas for Stress and Strain. McGraw-Hill, New York,1975.[22] W.C. Sabine. Collected papers on acoustics. Peninsula Publishing, LosAltos, CA., 1922.