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

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288 12. Walls, Enclosures, and BarriersFigure 12.4. Idealized plot of transmission loss versus frequency.where the critical frequency f ∗ is given byf ∗ = c λ ∗which corresponds to the grazing incidence θ = 90 ◦ . Also, there is a criticalangle θ ∗ , at which coincidence will occur, for any frequency above the criticalfrequency.Figure 12.5 contains a plot of critical frequencies against thickness for a numberof common construction materials. It must be realized that the critical frequencyFigure 12.5. Thickness versus critical frequency for a number of construction materials.(Source: Brüel and Kjær, 1980)
12.7 The Double-Panel Partition 289often falls in the range of speech frequencies, rendering some partitions nearlyuseless for providing privacy and preventing speech interference.From Equation (12.14), it is seen that the coincidence effect depends on characteristicsof the plate or panel and of the airborne sound wave. At coincidenceBω 2 sin 4 θ ∗= 1mc 4and inserting the above condition into Equation (12.14) yields the sound transmissioncoefficient for the coincidence conditionτ = τ ∗ 1=∗]mωη cos θ 2.[1 +2ρcThe corresponding transmission loss for the coincidence condition is( ) 1TL = TL ∗ ∗)fmη cos θ= 10 log = 20 log(1 + .τ ∗ ρcFrom the above equations, it would appear that τ ∗ = 1 and TL ∗ = 0 for undampedpanels (in which the loss factor η = 0). The above transmission loss equation ispremised on the theoretical behavior of an infinite plate, and the finite boundariesof actual structures such as windows and walls and the presence of damping inreal construction materials will produce a different response to sound waves.12.7 The Double-Panel PartitionA single-panel wall can exhibit resonant frequencies that fall below the rangeof speech frequencies. Most walls are constructed of two panels with an airspacebetween them, and they may yield low-frequency resonances in the speech range. Atypical interior partition consists of two gypsum board panels (ranging in thicknessfrom 1.3 cm to 1.9 cm, or from 0.5 in. to 0.75 in.) separated 9 cm (3.5 in.) by 5 cm ×10 cm (2 × 4) 1 wood or metal studs. In Figure 12.6 a double-panel configuration isshown; the two panels of mass per unit area m 1 and m 2 , respectively, are separatedby an airspace h. Because the air entrapped between the two panels behaves asa spring, a spring-mass analogy, shown in Figure 12.7, can be applied, with krepresenting the spring constant between two masses. The wall response modecan be depicted by two masses vibrating at the same frequency. A node (i.e. a“motionless” point) on the spring exists, thus effectively resolving the spring intotwo springs with spring constants (or spring rates) k 1 and k 2 , The natural frequencyof the dual-mass system is given byf n =√k1/m 1=2π√k2/m 2. (12.16)2π1 Lumber sizes are given by figures that are almost always nominal rather than representative of actualvalues. A two-by-four stud generally measures 1.75 × 3.5 in.
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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 243 and 244: 236 10. Physiology of Hearing and P
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
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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: 12.6 Coincidence Effect and Critica
Page 297 and 298: an ideal gas) varies in the followi
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
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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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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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