Introduction to Acoustics

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espectively, can be calculated from: δI,II = δ1 + δ2 � 2 (9.26) ± (δ1 − δ2) 2 S + 4 2 upon which δ1δ2 (A10 + S)(A20 + S) TI = 6.9/δI and TII = 6.9/δII . (9.27) Another important feature of the double-slope decay is how far down the knee point appears. If the opening area is large and/or the source or receiver is placed close to the opening, then a substantial exchange of energy can occur and the knee point may appear so early that even the EDT can be influenced by the decay from the coupled room with longer T. If the opening area is small, then the knee point appears late and far down on the curve, in which case the influence of the coupled room can only be perceived after final cords. This is the case with some of the existing concert halls equipped with coupled reverberation chambers. Further descriptions of coupled spaces can be found in [9.5]. 9.5.3 Absorption Data for Seats and Audiences Regardless of which reverberation formula is used, the availability of reliable absorption values is fundamental for the accurate prediction of T as well as of most other room acoustic parameters. Beyond the absorption values of various building materials (as listed in Table 11.1), realistic figures for the absorption of the chairs and seated audience are of special concern, because these elements normally account for most of the Acoustics in Halls for Speech and Music 9.5 Prediction of Room Acoustic Parameters 319 absorption in auditoria. The absorption of chairs – both with and without seated people – depends strongly on the degree of upholstery. Average values of absorption for three different degrees of chair upholstery have been published by Beranek [9.22] and quoted in Table 9.3.As mentioned earlier, chair absorption values for use specifically in Sabine calculations and for different types of hall geometries can be found in [9.21]. Sometimes audience absorption data are quoted as absorption area per chair or per person. However, as demonstrated by Beranek [9.3], the use of absorption coefficients multiplied by the area covered by the seats plus an exposed perimeter correction is more representative than absorption area per person, because audience absorption tends to vary proportionally with the area covered, while the absorption coefficient does not change much if the density of chairs is changed within that area. Minimizing the total sound absorption area is often attempted in auditoria for classical music in order to obtain a strong, reverberant sound field. One way to achieve this is not to make the row-to-row distance and the width of the chairs larger than absolutely necessary. Another factor is the seat design itself. Here one should aim at a compromise between minimum absorption and still a minimum difference between the absorption of the occupied and empty seat. This is facilitated by back rests not being higher than the shoulders of the seated person and only the surfaces covered by the person being upholstered. The rear side of the back rest should be made from a hard material like varnished wood. On the other hand, a minimum difference between the occupied and empty chair implies that the upholstery on the seat and back rest should be fairly thick (e.g., 80 mm on the Table 9.3 Absorption coefficients of seating areas in concert halls for three different degrees of upholstery; both empty and occupied (after [9.22]) Octave centre frequency (Hz) 125 250 500 1000 2000 4000 Heavily upholstered chairs 0.70 0.76 0.81 0.84 0.84 0.81 Unoccupied Heavily upholstered chairs 0.72 0.80 0.86 0.89 0.90 0.90 Occupied Medium upholstered chairs 0.54 0.62 0.68 0.70 0.68 0.66 Unoccupied Medium upholstered chairs 0.62 0.72 0.80 0.83 0.84 0.85 Occupied Lightly upholstered chairs 0.36 0.47 0.57 0.62 0.62 0.60 Unoccupied Lightly upholstered chairs 0.51 0.64 0.75 0.80 0.82 0.83 Occupied Part C 9.5
320 Part C Architectural Acoustics Part C 9.5 p (%) 100 80 60 40 20 0 –20 –40 –60 –80 –100 0 p (%) 100 80 60 40 20 0 –20 –40 –60 –80 –100 0 seat and 50 mm on the back rest), the bottom of the tipup seats should be perforated or otherwise absorptive, and when the seat is in its vertical position, there should be a wide opening between the seat and the back rest so that the sound can still access the upholstered areas. 9.5.4 Prediction by Computer Simulations Computer simulations take into account the geometry and actual distribution of the absorption materials in a room as well as the actual source and receiver positions. The results provided are values for all relevant acoustic parameters as well as the generation of audio samples for subjective judgments. Computer simulation is useful not only for the design of con- Left ear cert halls and theaters, but also for large spaces such as factories, open-plan offices, atria, traffic terminals, in which both reverberation, intelligibility and noisemapping predictions are of interest. Besides, they can be used in archaeological acoustics for virtual reconstruction of the acoustics of ancient buildings such as Roman theaters (http://server.oersted.dtu.dk/www/oldat/erato/). The first computer models appeared in the 1960s, and today a number of commercially available software packages are in regular use by acoustic consultants as well as by researchers all over the world. In computer simulations the room geometry is represented by a three-dimensional (3-D) computer-aided design (CAD) model. Thus, the geometry information can often be imported from a 3-D model file already cre- SPL at 1000Hz >15 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Time (s) Right ear 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Time (s) Fig. 9.14 Examples of output from a room acoustic simulation software package (ODEON); see text for explanation 13.5 12.8 12.0 11.3 10.5 9.8 9.0 8.3 7.5 6.7 6.0 5.2 4.5 3.7 3.0 2.2 1.5 0.7
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Springer Handbook of Acoustics
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Springer Handbook of Acoustics Thom
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Foreword The present handbook cover
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List of Authors Iskander Akhatov No
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Philippe Roux Université Joseph Fo
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XIV Contents 3.7 Attenuation of Sou
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XVI Contents 10 Concert Hall Acoust
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XVIII Contents 17.8 Physical Modeli
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XX Contents 24.5 Free-Field Microph
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XXII List of Abbreviations K KDP po
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Introduction 1. Introduction to Aco
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of noise have been the subject of c
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in order to understand how objectiv
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A Brief 2. A Brief History of Acous
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of 350 m/s for the speed of sound [
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number and relative strength of its
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To his contemporaries, Koenig was p
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Probably the most important use of
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piezoelectric ceramic compositions
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surveys together [2.46]. Masking of
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ther of computer music, since he de
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Basic 3. Linear Basic Linear Acoust
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M average molecular weight n unit v
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a) b) S v.n ∆t ∆S V |v| ∆t n
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temperature, q =−κ∇T , (3.16)
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The equivalent density M/V is conse
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Basic Linear Acoustics 3.3 Equation
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Because any vector field may be dec
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The latter and (3.84), in a manner
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assumed to have no ambient motion,
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Because the friction associated wit
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3.5 Waves of Constant Frequency One
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3.5.4 Time Averages of Products Whe
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as well as symmetry considerations,
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The auxiliary internal variables th
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Then the transient at a distant pos
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ω ′ = 0, and this is consistent
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1.0 10 -1 10 -2 10 -3 10 -4 10 -5 A
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This yields the interpretation that
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direction of propagation when a pla
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so the time-averaged incident energ
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Although the simple result of (3.31
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ut, also in keeping with the linear
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equation, the two differential equa
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Rodrigues relation, one has �1
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for the derivative.) In the asympto
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The differential scattering cross s
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elow) is F(t) = (2c) 1/2 �t −
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0.5 0 -0.5 -1.0 -1.5 0 Y0(η) (π/2
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is the Wronskian for the Bessel and
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The function qS is termed the sourc
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The appropriate identification for
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where jℓ is the spherical Bessel
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this subtlety taken into account, o
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U(x) Basic Linear Acoustics 3.15 Wa
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is ordinarily valid. With these ass
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along rays. These can be regarded a
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A(x0) x0 A(x) Fig. 3.53 Sketch of a
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possible, and one where neither the
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which is independent of the z-coord
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[3.108], and Carslaw [3.109]. In th
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where C(X)andS(X) are the Fresnel i
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Fig. 3.60 Characteristic diffractio
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of elastic solids, Trans. Camb. Phi
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3.101 J.B. Keller: Geometrical acou
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114 Part A Propagation of Sound Par
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Underwater 5. Underwater Acoustics
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5.1 Ocean Acoustic Environment The
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Long-Range Propagation Paths Figure
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tal direction, there is no loss ass
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equivalent circuit, as shown in Fig
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Attenuation á (dB/km) 1000 100 10
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5.2.5 Ambient Noise There are essen
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ubble natural acoustic resonance ω
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a bubbly medium (and for the simple
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As discussed, because detection inv
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(1/A)∇ 2 A ≪ K 2 )sothat(5.34)
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water, where the deep sound channel
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egion in the form p(r, z) = ψ(r, z
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5.4.6 Propagation and Transmission
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tegration interval. The source puls
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5.6 SONAR Array Processing Signal p
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former output is: �∞ b(θ,t) =
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Fig. 5.37 Angle-versus-time represe
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5.7 Active SONAR Processing Depth M
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a factor when there is a reverberan
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depth measurements that correspond
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along the cross-shelf track taken b
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time as a result of multiple paths,
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technique is very sensitive, and ex
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Fig. 5.57a,b Typical echogram obtai
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Frequency (Hz) 150 100 50 0 0 a) b)
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out. These data allow for study of
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5.59 G. Raleigh, J.M. Cioffi: Spati
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Physical 6. Physical Acou Acoustics
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where I is the intensity of the sou
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Wave velocity The wall exerts a dow
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destructively interfered with one a
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or: � � p2 � rms SPL = 10 log
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6.1.4 Wave Propagation in Solids Si
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where c is again the wave speed and
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measured. Some resonances are cause
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as 50 µmto5µm through one oscilla
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the number of false positives and m
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with the small mass), and frequency
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Laser Lens 1 Circular aperture Fig.
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Ground ring Insulator Sample Resist
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Energy ratio 1.0 0.8 0.6 0.4 Calcul
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terms. In this equation γ is the r
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directly. The nonlinearity paramete
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Thermoacoust 7. Thermoacoustics The
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Table 7.1 The acoustic-electric ana
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walls of the pores. (Positive G ind
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a) b) c) C reso d) δtherm e) p 0 U
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a) b) UA,l c) d) E 0 Q A Q A TA TA
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tor. This eliminates the need to le
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to this consumption of acoustic pow
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The traditional Stirling refrigerat
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Washington 1986) pp. 550-554, Softw
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258 Part B Physical and Nonlinear A
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a) c) S S -4.3 -2.8 -2.0 -3.5 -3dB
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Concert Hall Acoustics Based on Sub
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a model of the auditory-brain syste
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Building 11. Building Acou Acoustic
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Pressure Maximum Minimum 0 D Distan
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Table 11.1 Absorption coefficients
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Absorption coefficient α 1 0 Frequ
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is of key importance in rooms where
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Table 11.4 Transmission loss and ST
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TL of wall - (TL of door, window or
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Table 11.7 Generalized noise reduct
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Masking sound pressure level (dB) 5
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As for the room criterion (RC) meth
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11.5 Noise Control Methods for Buil
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Neoprene pads (30 durometer) with a
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Concrete Caulk around perimeter Vib
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Trim board to conceal gap (fasten o
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Gypsum board partition (as schedule
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Double-layer ribbed or waffle neopr
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11.6 Acoustical Privacy in Building
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Table 11.9 AI,SIIandPIforopenplanof
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Electronic sound masking in plenum
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E 1179 Standard Specification for S
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430 Part D Hearing and Signal Proce
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Psychoacoust 13. Psychoacoustics Ps
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Absolute threshold (dB SPL) 100 90
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the signal. By using this off-cente
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is as a crude indicator of the exci
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Relative response (dB) 100 90 80 70
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In a variation of this procedure, t
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Level of matching noise (dB) 100 90
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13.4 Temporal Processing in the Aud
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Most models include an initial stag
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The components were either uniforml
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(Frequency DL)/ERBN 0.2 0.1 0.05 0.
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elaborate place models have been pr
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13.6 Timbre Perception 13.6.1 Time-
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the duplex theory of sound localiza
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harmonic (by shifting the frequency
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sive. While some studies have been
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sentences (see Fig. 13.20). They va
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components is usually only perceive
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References 13.1 ISO 389-7: Acoustic
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13.74 D. Ronken: Monaural detection
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asymmetric function, J. Acoust. Soc
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13.211 J. Vliegen, A.J. Oxenham: Se
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534 Part E Music, Speech, Electroac
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The 16. The Human Human Voice in Sp
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uation, the effect of gravity is in
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piratory muscles (the internal inte
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Mean Ps (cm H2O) 50 40 30 20 10 0 D
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Glottal flow Closed Opening Open Cl
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Transglottal airflow (l/s) 0.4 0.2
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Mean spectrum level (dB) -30 -40 -5
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20 10 0 -10 -20 -30 -40 -50 0 i y u
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Mean level (dB) 0 -10 -20 -30 -40 1
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This topic was addressed by Ladefog
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Fig. 16.29 Acoustic consequences of
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Bass i e u Alto Tenor o ε œ æ Th
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100 80 60 40 20 0 -20 100 80 60 40
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tours for [� ]and[Ù ] sampled at
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Rapp [16.100] asked three native sp
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Utterance command T0 T3 Accent comm
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The # symbol indicates the possibil
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Second formant frequency (Hz) 2500
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tional rather than absolute (à la
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16.7 P. Ladefoged, M.H. Draper, D.
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esonance imaging: Vowels, J. Acoust
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16.139 A. Eriksson: Aspects of Swed
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Computer 17. Computer Mu Music This
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Quantum step Amplitude Quantization
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Some might notice that linear inter
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pers, textbooks, patents, etc. Furt
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0:00.0 0.5 0 Computer Music 17.3 Ad
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(0,0) (0,1) (1,1) (0,2) (1,2) (0,3)
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synthesizing vocoder. The main diff
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x(n) + z -1 z -1 Scattering junctio
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230 Hz FOF 1100 Hz FOF 1700 Hz FOF
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0 y + - Computer Music 17.8 Physica
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-1 (1-ß )×length Velocity + Veloc
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0 -30 (dB) -60 0 1.5 3 4.5 (kHz) Fi
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17.10 Composition The history of co
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and variance of the features can be
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17.20 J.L. Kelly Jr., C.C. Lochbaum
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Audio 18. Audio and Electroacoustic
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Alexander Graham Bell filed his pat
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on magnetic stripes. A common arran
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60 40 20 0 SPL-sound pressure level
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Interaural intensity difference (dB
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with equalization, without incurrin
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Fig. 18.8 Sine wave with crossover
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18.3.8 Dynamic Range Dynamic range
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Directly actuated type Diaphragm ty
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effective pickup pattern of the arr
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attempts to apply complementary com
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Most of the issues relating to spea
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nificant design considerations. At
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Some appreciation of the performanc
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pre-digital reverberators were elec
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and ‘s’ in English text - may b
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content of rest of the signal spect
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cross the head, in opposite directi
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18.2 J. Sterne: The Audible Past (D
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18.71 T. Sporer: Creating, assessin
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786 Part F Biological and Medical A
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Medical 21. Medical Acous Acoustics
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21.1 Introduction to Medical Acoust
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Auscultation location Right & left
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portance. The Strouhal number has b
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Fig. 21.3 Phono-cardiograph transdu
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Amplitude 8 6 4 2 0 -2 -4 -6 Displa
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λ1 = c1 / fus θ1 λ2 = c2 / fus
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lood flow can be resolved if the si
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vided in the image thickness direct
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not as predicted, because the wave
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Fig. 21.18a,b Quadrature Doppler de
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a) b) c) 100 0 V mV 10 0 a = 13 a =
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Ultrasound contact gel Position enc
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a) 10 cm b) c) 10 cm Fig. 21.32a-c
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a) Pin B Pin A Ultrasound line b) M
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Organ Patient Ultrasound transducer
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systems cannot tell the difference
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40 µm can be resolved. For a 10 kH
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a) b) c) d) Medical Acoustics 21.4
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Fig. 21.54 Doppler spectral wavefor
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10 20 30 10 20 30 Pre-exercise B-mo
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Vibrations in a punctured artery De
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the veins and diffuse into the inte
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21.5.3 Agitated Saline and Patent F
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transported by those cells and/or r
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1 0.8 0.6 0.4 0.2 0 Relative power
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High intensity focused ultrasound h
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a) b) c) Fig. 21.74a-c B-mode imagi
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provided simple metrics for the lik
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thickness of the carotid arteries,
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Structural 22. Structural Acoustics
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Structural Acoustics and Vibrations
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Magnitude (arb. units) 1.4 1.2 1.0
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This does not include the case wher
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the mass matrix is taken to be cons
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Magnitude (dB) -10 -30 -50 0 1 2 3
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where D(ω) = ω 4 − 2iω 3�
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form y(x, t) = � Φn(x)qn(t) . (2
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first to solve the wave equation (2
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5 3 1 -1 -3 -5 0 1 2 3 4 5 6 7 8 9
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conditions at each end) are necessa
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from which we can derive through (2
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In this case, the eigenfrequencies
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of radiation modes and their link w
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Finally, the displacement is ˜ξ(x
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notes the value of this eigenmode a
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Pm = ˙Q H [Rs + Ra] ˙Q , (22.262)
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where and Ra = 2ζaω0 M Z(s) = zL
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Radiated Power. The mean acoustic p
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(22.318) can be written ξ(x, y, t)
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Denoting the eigenfrequencies and e
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Magnitude (arb. units) 3 2 1 0 -1 -
Page 942 and 943:
for any real symmetric tensor Xij.
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F(N) 1 0.5 0 -0.5 -1 -1 -0.8 -0.6 -
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whose solution is θ1 = A cos ωτ.
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4.5 3.5 2.5 1.5 A 0.5 0 0.5 1.0 1.5
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Equations (22.423) are usually writ
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3. As the amplitude reaches the top
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Shallow Spherical Shells and Plates
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22.20 L. Cremer, M. Heckl: Structur
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Noise Noise is discussed in terms o
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where the overbars represent time a
Page 962 and 963:
Typical outdoor setting A-weighted
Page 964 and 965:
90 dB(A)” is widely used, and imp
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Microphone, amplifier and A/D conve
Page 968 and 969:
When each segment of the measuremen
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found from � LW = Lp + 10 log A +
Page 972 and 973:
surement method is the ultimate use
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An intensity analyzer is more compl
Page 976 and 977:
23.2.5 Criteria for Noise Emissions
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Table 23.5 Table of limit values fr
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a) Air flows freely to rotor Weak t
Page 982 and 983:
Static efficiency normalized to its
Page 984 and 985:
ful applications. Good results are
Page 986 and 987:
Table 23.8 Crossover speeds for var
Page 988 and 989:
Reduction of airplane engine noise
Page 990 and 991:
A variety of materials are used to
Page 992 and 993:
∆LF (dB) 0 -10 -20 α -30 0.05 0.
Page 994 and 995:
Absorption coefficient 1.0 0.8 0.6
Page 996 and 997:
high enough that there is little so
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23.4.4 Criteria for Noise Immission
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Table 23.10 (cont.) Some features o
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Noise 23.4 Noise and the Receiver 1
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view of administrative procedures r
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provides recommendations for a foll
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sound power levels of noise sources
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23.68 ISO: ISO 9296:1988 Acoustics
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in impedance tubes - Part 2: Transf
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23.194 Commission of the European C
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1022 Part H Engineering Acoustics P
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Sound 25. Intens Sound Intensity So
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Under such conditions the intensity
Page 1050 and 1051:
a) Pressure and particle velocity 0
Page 1052 and 1053:
τ is a dummy time variable. The ca
Page 1054 and 1055:
Error in intensity (dB) 5 0 -5 -10
Page 1056 and 1057:
8 7 6 5 4 3 2 1 0 -1 -2 -3 Error du
Page 1058 and 1059:
crophones are calibrated with a pis
Page 1060 and 1061:
Sound power level (dB re 1 pW) 72 7
Page 1062 and 1063:
it is relatively straightforward si
Page 1064 and 1065:
intensity normal to the source. Thi
Page 1066 and 1067:
25.9 W. Maysenhölder: The reactive
Page 1068 and 1069:
25.77 ISO: ISO 11205 Acoustics - No
Page 1070 and 1071:
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Optical 27. Optical Methods Metho f
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course also present in ordinary hol
Page 1096 and 1097:
Optical Methods for Acoustics and V
Page 1098 and 1099:
Page 1100 and 1101:
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50 100 150 200 250 300 350 400 450
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a) b) Optical Methods for Acoustics
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nm 1000 0 -1000 150 y (mm) 100 50 O
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Page 1110 and 1111:
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Laser Optical Methods for Acoustics
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References 27.1 E.F.F. Chladni: Die
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27.75 E.-L.Johansson, L. Benckert,
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Page 1130 and 1131:
About the Authors Iskander Akhatov
Page 1132 and 1133:
Neville H. Fletcher Chapter F.19 Au
Page 1134 and 1135:
Brian C. J. Moore Chapter D.13 Univ
Page 1136 and 1137:
Detailed Contents List of Abbreviat
Page 1138 and 1139:
3.8.3 Acoustic Power ..............
Page 1140 and 1141:
4.8.3 Typical Speed of Sound Profil
Page 1142 and 1143:
7.3 Engines .......................
Page 1144 and 1145:
10 Concert Hall Acoustics Based on
Page 1146 and 1147:
13.4 Temporal Processing in the Aud
Page 1148 and 1149:
15.2.5 String-Bridge-Body Coupling
Page 1150 and 1151:
19.6 Birds ........................
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22.4.5 Combinations of Elementary S
Page 1154 and 1155:
24.8 Overall View on Microphone Cal
Page 1156 and 1157:
Subject Index 3 dB bandwidth 463 A
Page 1158 and 1159:
British Medical Ultrasound Society
Page 1160 and 1161:
electric circuit analogues - acoust
Page 1162 and 1163:
hyperspeech 703 hypospeech 703 I IA
Page 1164 and 1165:
- participation factors 909 - stiff
Page 1166 and 1167:
- musical instruments 541 - musical
Page 1168 and 1169:
- nonlinear vibrations 957 - plate
Page 1170 and 1171:
subjective preference theory 353 su
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Introduction to Acoustics

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