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

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290 12. Walls, Enclosures, and BarriersFigure 12.6. A double-panel partition.The individual spring constants are related to the spring constant of the compositespring by1k = 1 + 1 . (12.17)k 1 k 2Eliminating k 2 between Equations (12.16) and (12.17) results ink 1 = k m 1 + m 2.m 2Inserting the last expression into the first portion of Equation (12.16) yields thenatural frequency f n of the system:√k m 1 + m 2mf n = 1 m 2. (12.18)2πIn order to establish the effective spring constant of the air between the panels,it will be assumed that an isentropic process constitutes the action of sound waves,since the pressure changes occur too rapidly for an isothermal process to take place.From thermodynamics, for an isentropic process the pressure p of air (consideredFigure 12.7. Spring-mass analogy of the double-panel partition of Figure 12.6.
an ideal gas) varies in the following manner:12.7 The Double-Panel Partition 291pv γ = constant (12.19)where v represents the specific volume (equal to the reciprocal of density) and γ ,the ratio of specific heats. Differentiating Equation (12.19) givesdpdv =−γ p v . (12.20)Sound waves cause the ambient pressure and specific volume of air to vary onlyslightly from the quiescent values of p 0 and v 0 , and thus the instantaneous valuesp and v differ very little from p 0 and v 0 in Equation (12.20). Because the massof air entrapped between the panels remains constant, the ratio of panel displacement(arising from the sound pressure pushing on the panels) dh to the original(quiescent) spacing h 0 should equal the ratio of the change of specific volume tothe quiescent value of the specific volume:dh= dv(12.21)h 0 v 0But the spring constant represents the force per unit displacement, or for a unitarea of the wallk =− dpdh . (12.22)Combining Equations (12.21) and (12.22) and dropping the subscripts (sinceh 0 ≈ h, p 0 ≈ p), we now havek =− γ phwhich, upon inserting into Equation (12.19), gives√γ p m 1 + m 2hmf n =1 m 2.2πSetting γ = 1.4 and p = 101.325 kPa (the standard atmosphere), the lowfrequencyresonance of the double-panel wall may now be found from√m1 + mf n = 602. (12.23)hm 1 m 2The surface masses m 1 and m 2 are given in kg/m 2 and the panel spacing h inmeters.Example Problem 2Predict the transmission loss for an 8-in. wall of poured concrete for 800-Hz sound.The concrete has a density of approximately 150 lb/ft 3 (2406 kg/m 3 ).
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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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Page 245 and 246: 238 10. Physiology of Hearing and P
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Page 249 and 250: 11Acoustics of Enclosed Spaces:Arch
Page 251 and 252: 11.2 Sound Fields 245Figure 11.1. P
Page 253 and 254: 11.4 Sound Intensity Growth in a Li
Page 255 and 256: 11.5 Sound Absorption Coefficients
Page 257 and 258: 11.6 Growth of Sound with Absorbent
Page 259 and 260: 11.7 Decay of Sound 253Following Sa
Page 261 and 262: 11.8 Decay of Sound in Dead Rooms 2
Page 263 and 264: 11.9 Reverberation as Affected by S
Page 265 and 266: 11.13 Sound Levels due to Direct an
Page 267 and 268: 11.15 Concert Halls and Opera House
Page 269 and 270: Figure 11.9. A view of the Boston S
Page 277 and 278: 11.16 Band Shells and Outdoor Audit
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Page 281 and 282: 11.17 Subjective Preferences in Sou
Page 283 and 284: References 277preferred subsequent
Page 285 and 286: Problems for Chapter 11 279Siebein,
Page 287 and 288: 12Walls, Enclosures, and Barriers12
Page 289 and 290: 12.3 Mass Control Case 283Figure 12
Page 291 and 292: 12.5 Effect of Frequencies on Sound
Page 293 and 294: 12.6 Coincidence Effect and Critica
Page 295: 12.7 The Double-Panel Partition 289
Page 299 and 300: 12.8 Measuring Transmission Loss 29
Page 301 and 302: 12.10 Combined Sound Transmission C
Page 303 and 304: 12.11 Noise Insulation Ratings 297F
Page 305 and 306: 12.11 Noise Insulation Ratings 299s
Page 307 and 308: 12.12 Noise Reduction of a Wall 301
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Page 311 and 312: 12.14 Enclosures 305to the extent t
Page 313 and 314: 12.14 Enclosures 307and similarly f
Page 315 and 316: 12.15 Small Enclosures 309walls. Ac
Page 317 and 318: 12.16 Acoustic Barriers 311Figure 1
Page 319 and 320: 12.16 Acoustic Barriers 313In the c
Page 321 and 322: Equation (12.67) becomes(11D = λ+
Page 323 and 324: Problems for Chapter 12 3173. A 0.7
Page 325 and 326: 13Criteria and Regulations forNoise
Page 327 and 328: 13.3 The Occupational Safety and He
Page 329 and 330: 13.4 Perception of Noise 323inspect
Page 331 and 332: 13.6 Indoor Noise Criteria 325accou
Page 333 and 334: 13.6 Indoor Noise Criteria 327Room
Page 335 and 336: 13.7 Equivalent Sound Level, Day-Ni
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Page 339 and 340: Composite Noise Rating13.9 Rating o
Page 341 and 342: 13.10 Evaluation of Traffic Noise 3
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Page 345 and 346: Highway Construction Noise13.10 Eva
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13.10 Evaluation of Traffic Noise 3
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13.10 Evaluation of Traffic Noise 3
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13.11 Evaluation of Community Noise
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13.12 Guidelines and Regulations in
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References 353Computer Program, HIC
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Problems for Chapter 13 355Problems
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14Machinery Noise Control14.1 Intro
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14.4 Fan or Blower Noise 359Table 1
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14.4 Fan or Blower Noise 361Figure
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14.6 Pumps and Plumbing Systems 367
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14.6 Pumps and Plumbing Systems 369
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14.8 Gears 371fromwheref BRC = N r
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14.8 Gears 373Figure 14.7. Gear noi
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14.8 Gears 375Figure 14.8. Gear tra
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14.8 Gears 377The subscripts 1 and
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14.10 Ball and Roller Bearings 379l
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14.10 Ball and Roller Bearings 381c
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14.11 Other Mechanical Drive Elemen
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Belt Drivesf CL = n 1N 1 2400 × 12
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14.12 Gas-Jet Noise 387said to be c
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14.12 Gas-Jet Noise 389power discha
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Solution14.12 Gas-Jet Noise 391Usin
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14.13 Gas Jet Noise Control 393Solu
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14.13 Gas Jet Noise Control 395Figu
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14.13 Gas Jet Noise Control 397Figu
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14.14 Mufflers and Silencers 399Fig
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(1 + m)A I 1=A 314.14 Mufflers and
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14.14 Mufflers and Silencers 403Let
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References 405Figure 14.21 illustra
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Problems for Chapter 14 407the nois
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15Underwater Acoustics15.1 Sound Pr
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15.3 Speed of Sound in Seawater 411
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15.4 Velocity Profiles in the Sea 4
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15.4 Velocity Profiles in the Sea 4
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15.5 Underwater Transmission Loss 4
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15.6 Parametric Variation of Absorp
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15.8 Underwater Refraction 421Figur
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15.9 Mixed Layer 423When G is const
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15.11 Sonar Transducers and Their P
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Example Problem 115.12 The Sonar Eq
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Active and Passive Equations15.12 T
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15.13 Noise, Echo, and Reverberatio
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15.13 Noise, Echo, and Reverberatio
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15.14 Transient Form of Sonar Equat
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Example Problem 315.16 Shortcomings
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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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