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

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48 3. Sound Wave Propagation and Characteristicsalways zero, since the mean rarefaction equals the mean compression. A simpleway to measure the degree of disturbance is to square the values of the soundpressure disturbance over a period of time, thereby eliminating the counter-effectsof negative and positive disturbances by rendering them always positive. The rootmean-squaresound pressure p rms can be defined byp rms = √ √ ∫ τ(p) 2 0=p2 dt∫ τ0 dt (3.20)where τ is the time interval of measurement and p the instantaneous pressure. Fora simple cosine wave over an interval of period T = 2π/ω, there results√ ∫ Tp0rms =p2 m cos2 k(x − ct) dtT= p m√2. (3.21)The sound pressure as portrayed by the oscillation of the pressure above andbelow the atmospheric pressure is detected by normal human ear at levels as lowas approximately 20 μPa (the SI unit of pressure is the pascal, abbreviated Pa,equivalent to 1.0 N/m 2 ). 1 Because p rms could vary over a wide range of ordersof magnitude, it would be cumbersome to use it as the measure of loudness. Atthe threshold of pain, p rms would reach approximately 40,000,000 μPa! The blastoffpressure in the vicinity of the launching pad of a Titan rocket can exceedup to a thousandfold the threshold of pain (i.e., 40 kPa). It is therefore moreconvenient to use the decibel as the folding-scale measure of loudness. This unit isdefined by( ) 2 ( )prmsprmsL p = 10 log = 20 log(3.22)p 0 p 0whereL p = sound pressure level (dB)log = common (base-ten) logarithmp 0 = 20 × 10 −6 Pa = the reference pressure.From the context of Equation (3.22) it can be established that the doubling ofa root-mean-square pressure corresponds to approximately 6 dB increase in thesound pressure level. In order to determine the sound pressure level from a givenvalue of L p , Equation (3.22) can be rewritten asorp rmsp 0= 10 L p20p rms = 20 × 10 L p20 −61 One standard atmosphere equals 101.325 kPa.
3.12 Decibel Additions, Subtracting, and Averaging 49Figure 3.11. Sound pressure levels and corresponding pressures of various sound sources.Figure 3.11 illustrates the range of the decibel scale in terms of measured valuesof common sound sources. The audible range of sound, which encompasses musicand speech, is shown delineated in Figure 3.12 in terms of sound pressure levelsand frequencies.3.12 Decibel Additions, Subtracting, and AveragingMost sound pressure levels do not arise from single sources, nor do they remainconstant in time. Mathematical procedures must be used to add, subtract, andaverage decibels. From the definition of Equation (3.22) it is apparent that decibelsfrom single-noise sources do not add or subtract directly. If we wish to add sound
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THE SCIENCE ANDAPPLICATIONS OFACOUS
Page 8 and 9: xPrefaceReferencesBacon, Sir Franci
Page 10 and 11: xiiContents16. Ultrasonics 44317. C
Page 12: 2 1. A Capsule History of Acoustics
Page 15 and 16: 1. A Capsule History of Acoustics 5
Page 17 and 18: 1. A Capsule History of Acoustics 7
Page 19: 1. A Capsule History of Acoustics 9
Page 22 and 23: 12 1. A Capsule History of Acoustic
Page 24 and 25: 14 2. Fundamentals of AcousticsFigu
Page 26 and 27: 16 2. Fundamentals of Acoustics2.2
Page 28 and 29: 18 2. Fundamentals of Acousticsof t
Page 30 and 31: 20 2. Fundamentals of AcousticsQ z+
Page 32 and 33: 22 2. Fundamentals of Acousticsin t
Page 34 and 35: 24 2. Fundamentals of AcousticsWe c
Page 36 and 37: 26 2. Fundamentals of Acoustics(2)
Page 38 and 39: 28 2. Fundamentals of AcousticsEqua
Page 40 and 41: 30 2. Fundamentals of Acoustics11.
Page 42 and 43: 32 3. Sound Wave Propagation and Ch
Page 62: 52 3. Sound Wave Propagation and Ch
Page 65 and 66: 3.14 Performance Indices for Enviro
Page 67 and 68: 3.14 Performance Indices for Enviro
Page 69 and 70: or in terms of complex exponential
Page 71 and 72: 3.17 Sound Intensity 61Here the sur
Page 73 and 74: 3.18 The Monopole Source 63The thre
Page 75 and 76: 3.21 Energy Density 653.20 The Hemi
Page 77 and 78: References 67medium. The time avera
Page 79 and 80: Problems for Chapter 3 69(a) the wa
Page 81 and 82: 4Vibrating Strings4.1 IntroductionI
Page 83 and 84: 4.4 General Solution of the Wave Eq
Page 85 and 86: 4.6 Simple Harmonic Solutions of th
Page 87 and 88: 4.7 Standing Waves 77Figure 4.3. Di
Page 89 and 90: 4.8 The Effect of Initial Condition
Page 91 and 92: 4.10 Forced Vibrations in an Infini
Page 93 and 94: 4.11 Strings of Finite Lengths: For
Page 95 and 96: References 854.12 Real Strings: Fre
Page 97 and 98: Problems for Chapter 4 878. A devic
Page 99 and 100: 90 5. Vibrating BarsFigure 5.1. A b
Page 101 and 102: 92 5. Vibrating BarsSettingc 2 = E/
Page 103 and 104: 94 5. Vibrating BarsThe allowable f
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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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Highway Construction Noise13.10 Eva
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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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