THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

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388 14. Machinery Noise ControlNoise is generated from gas jets through the creation of fluctuating pressures fromthe turbulence and shearing stresses, as the high-velocity gas impacts with theambient gas. In establishing the theory of aeroacoustics, the nonlinear effects ofthe momentum flux ρu i u j (i.e., the rate of transport of any momentum ρu i acrossa unit area by any velocity component u j ) cannot be neglected as they were forlinear acoustics. The momentum flux acts as a stress, since the rate of changeof momentum constitutes a force. This momentum flux ρu i u j generates soundas a distribution of time-varying stresses. The forces between the airflow andits boundary radiate sound as distributed dipoles, and the stresses (which act onfluid elements with equal and opposite dipole-type forces) radiate as distributedquadrupoles.The nature of the noise from jets cannot be accurately predicted, owing to thecomplex nature of the jet itself and the uncertainties associated with turbulence,nozzle configuration, temperature vacillations, and so on. However, first-orderestimates can be derived from empirical data obtained for the most part fromexperimentation in the aviation industry. The earliest measurements of jet noisedemonstrated that intensity and noise power varied very closely with the eighthpower of the jet exit velocity (Lighthill’s eighth power law), and it is now generallyagreed that the overall sound power P can be expressed asP = Kρ 0U 8 D 2c 5 0(14.41)where K is a constant, with a value 3–4; D is the jet diameter (in meters); U isthe jet flow velocity (m/s); ρ 0 is the density of ambient air (kg/m 3 ); and c 0 is theambient speed of sound (m/s). The factor ρ 0 U 8 D 2 c −50is often called Lighthill’sparameter. Because the kinetic power of a jet is proportional to 1 2 ρ 0U 2 · UD 2 , thefraction of the power converted into noise is the noise-generating efficiency η,η ∝ M 5 (14.42)where M = U/c 0 , the Mach number of the flow referenced to the ambient speedof sound.Aerodynamic noise can be modeled as monopoles, dipoles, and quadrupoles.A jet pulse through a nozzle or discharge from HVAC ducts can be modeled as amonopole. In fans and compressors, the turbulent flow generally encounters rotoror stator blades, grids, and baffles; this type of flow can be modeled as a dipole.Quadrupole modeling applies to noise occurring from turbulent mixing in jetswhere there is no interaction with confining surfaces.The velocity term U in Equation (14.41) is the fluctuating velocity which variesthroughout the jet stream. Consequently, U is not easily measured nor amenableto analytical treatment. But we can consider the average velocity V and assumethat the size of the energy-bearing eddies are of the same order of magnitude as thejet diameter, and the total radiated acoustic power P is proportional to the kineticenergy of the jet flow. The total radiated power is simply a fraction of the total
14.12 Gas-Jet Noise 389power discharged from the nozzle, i.e.,whereP = ε M5 ρ 0 V 3 A2in watts (14.43)V = average flow velocity through the nozzle, m/sM = Mach number of the flow = V/c, dimensionlessρ 0 = density of ambient airA = nozzle areaε = constant of proportionality, in the order of 10 −4Equation (14.43) constitutes a first-order approximation that is applicable tomany industrial situations where the average velocity of the jetstream lies in therange of 0.15c < V ≤ c. The efficiency factor εM 5 is plotted from empirical datain Figure 14.12 over a range of Mach numbers. As a reflection of the uncertaintyassociated with turbulence, temperature, and so forth, the efficiency factor is givenas a range.Figure 14.12. Efficiency factor εM 5 versus Mach number.
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THE SCIENCE ANDAPPLICATIONS OFACOUS
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xPrefaceReferencesBacon, Sir Franci
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xiiContents16. Ultrasonics 44317. C
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2 1. A Capsule History of Acoustics
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1. A Capsule History of Acoustics 5
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12 1. A Capsule History of Acoustic
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14 2. Fundamentals of AcousticsFigu
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16 2. Fundamentals of Acoustics2.2
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18 2. Fundamentals of Acousticsof t
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20 2. Fundamentals of AcousticsQ z+
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22 2. Fundamentals of Acousticsin t
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24 2. Fundamentals of AcousticsWe c
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26 2. Fundamentals of Acoustics(2)
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28 2. Fundamentals of AcousticsEqua
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30 2. Fundamentals of Acoustics11.
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32 3. Sound Wave Propagation and Ch
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3.14 Performance Indices for Enviro
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3.14 Performance Indices for Enviro
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or in terms of complex exponential
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3.17 Sound Intensity 61Here the sur
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3.18 The Monopole Source 63The thre
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3.21 Energy Density 653.20 The Hemi
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References 67medium. The time avera
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Problems for Chapter 3 69(a) the wa
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4Vibrating Strings4.1 IntroductionI
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4.4 General Solution of the Wave Eq
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4.6 Simple Harmonic Solutions of th
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4.7 Standing Waves 77Figure 4.3. Di
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4.8 The Effect of Initial Condition
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4.10 Forced Vibrations in an Infini
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4.11 Strings of Finite Lengths: For
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References 854.12 Real Strings: Fre
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Problems for Chapter 4 878. A devic
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90 5. Vibrating BarsFigure 5.1. A b
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92 5. Vibrating BarsSettingc 2 = E/
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94 5. Vibrating BarsThe allowable f
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96 5. Vibrating Barsthe acceleratio
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98 5. Vibrating BarsFigure 5.5. Loc
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100 5. Vibrating Barsmore difficult
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102 5. Vibrating BarsFigure 5.7. An
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104 5. Vibrating Barsthe light beam
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106 5. Vibrating BarsFigure 5.8. Tr
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108 5. Vibrating BarsFigure 5.10. T
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110 5. Vibrating Barsof 0.005 m dia
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112 6. Membrane and PlatesFigure 6.
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114 6. Membrane and PlatesBecause t
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116 6. Membrane and PlatesThe left-
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118 6. Membrane and PlatesTable 6.1
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120 6. Membrane and PlatesIn real a
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122 6. Membrane and PlatesTable 6.2
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124 6. Membrane and PlatesAt low fr
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126 6. Membrane and PlatesThe elast
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128 6. Membrane and PlatesFor the f
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130 6. Membrane and Plates(b) Deter
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132 7. Pipes, Waveguides, and Reson
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152 8. Acoustic Analogs, Ducts, and
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9Sound-Measuring Instrumentation9.1
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9.3 Microphones 175Figure 9.1. A cu
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SolutionEquation (9.3) is applied t
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9.5 Selection and Positioning of Mi
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9.6 Vector Sound Intensity Probes 1
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9.8 Proper Procedures for Using the
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9.8 Proper Procedures for Using the
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Example Problem 39.10 Dosimeters 18
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9.11 Noise Measurement in Selected
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9.11 Noise Measurement in Selected
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9.12 Real Time Analysis 193analyzer
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9.13 Fast Fourier Transform Analysi
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9.14 Data Windows and Selection of
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9.16 Measurement Error 199whereβ =
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9.18 Measurement of Sound in a Free
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9.20 Sound Power Measurement in a D
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9.20 Sound Power Measurement in a D
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9.23 The Addition Method for Measur
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References 209acoustical output and
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Problems for Chapter 9 2112. Determ
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214 10. Physiology of Hearing and P
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11Acoustics of Enclosed Spaces:Arch
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11.2 Sound Fields 245Figure 11.1. P
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11.4 Sound Intensity Growth in a Li
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11.5 Sound Absorption Coefficients
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11.6 Growth of Sound with Absorbent
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11.7 Decay of Sound 253Following Sa
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11.8 Decay of Sound in Dead Rooms 2
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11.9 Reverberation as Affected by S
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11.13 Sound Levels due to Direct an
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11.15 Concert Halls and Opera House
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Figure 11.9. A view of the Boston S
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11.16 Band Shells and Outdoor Audit
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11.16 Band Shells and Outdoor Audit
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11.17 Subjective Preferences in Sou
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References 277preferred subsequent
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Problems for Chapter 11 279Siebein,
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12Walls, Enclosures, and Barriers12
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12.3 Mass Control Case 283Figure 12
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12.5 Effect of Frequencies on Sound
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12.6 Coincidence Effect and Critica
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12.7 The Double-Panel Partition 289
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an ideal gas) varies in the followi
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12.8 Measuring Transmission Loss 29
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12.10 Combined Sound Transmission C
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12.11 Noise Insulation Ratings 297F
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12.11 Noise Insulation Ratings 299s
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12.12 Noise Reduction of a Wall 301
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12.12 Noise Reduction of a Wall 303
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12.14 Enclosures 305to the extent t
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12.14 Enclosures 307and similarly f
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12.15 Small Enclosures 309walls. Ac
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12.16 Acoustic Barriers 311Figure 1
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12.16 Acoustic Barriers 313In the c
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Equation (12.67) becomes(11D = λ+
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Problems for Chapter 12 3173. A 0.7
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13Criteria and Regulations forNoise
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13.3 The Occupational Safety and He
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13.4 Perception of Noise 323inspect
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13.6 Indoor Noise Criteria 325accou
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13.6 Indoor Noise Criteria 327Room
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13.7 Equivalent Sound Level, Day-Ni
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13.7 Equivalent Sound Level, Day-Ni
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Composite Noise Rating13.9 Rating o
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13.10 Evaluation of Traffic Noise 3
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Page 359 and 360: References 353Computer Program, HIC
Page 361 and 362: Problems for Chapter 13 355Problems
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Page 381 and 382: 14.8 Gears 375Figure 14.8. Gear tra
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15.17 Theoretical Target Strength o
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Problems for Chapter 15 441Wilson,
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444 16. Ultrasonicscatching small i
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446 16. UltrasonicsPlanck constant
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448 16. UltrasonicsEquation (16.5)
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450 16. UltrasonicsFigure 16.1. Sou
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452 16. Ultrasonicsthe positive hal
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454 16. Ultrasonicson each and ever
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456 16. Ultrasonicscomplete as a li
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458 16. Ultrasonicsinitial of their
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460 16. Ultrasonicsoptic axis, deno
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462 16. Ultrasonicstransducer, it h
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464 16. UltrasonicsTable 16.1. Valu
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466 16. Ultrasonicsthe mechanical r
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468 16. UltrasonicsThe Physics of M
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470 16. UltrasonicsFigure 16.7. The
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472 16. Ultrasonicscurvilinear arra
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474 16. Ultrasonics(a)amplitudeinpu
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476 16. Ultrasonicsslow to allow th
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478 16. Ultrasonics5. In the cases
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480 17. Commercial and Medical Ultr
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510 18. Music and Musical Instrumen
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Figure 18.7. The frequencies of the
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Figure 18.20. The violin octet deve
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570 19. Sound ReproductionAlbert, a
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572 19. Sound ReproductionD. Magnet
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574 19. Sound Reproductionon, machi
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576 19. Sound ReproductionIt is fai
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578 19. Sound ReproductionINNER SUS
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580 19. Sound Reproductiontuned ape
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582 19. Sound Reproductionuse of MP
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584 19. Sound ReproductionDickason,
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586 20. Vibration and Vibration Con
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618 21. Nonlinear Acousticsby∇ 2
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620 21. Nonlinear Acousticsmay be i
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622 21. Nonlinear Acousticswhereδ
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624 21. Nonlinear AcousticsThe shoc
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626 21. Nonlinear AcousticsBut the
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Appendix APhysical Properties of Ma
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Appendix A. Physical Properties of
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Appendix BBessel FunctionsB.1 The B
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B.8 Tables of Bessel Functions, Zer
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Appendix CUsing Laplace Transforms
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C.3 Solving Differential Equations
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C.4 Equations with Multiple-Order R
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SolutionC.5 Equations with Complex
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C.5 Equations with Complex Roots 64
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SolutionC.5 Equations with Complex
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650 IndexAuditoriums, design of, 26
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652 IndexElectrostatic speakers, 58
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654 IndexKey notation, 518Kinetic e
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656 IndexPascal (unit), 48Percent i
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658 IndexSound intensity growth in
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660 IndexWater-hammer arresters, 37
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