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

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632 Appendix A. Physical Properties of MatterA.4. (Continued)Conversely,To Convert Into Multiply by Multiply byin. 2 (square inch) ft 2 6.945 × 10 −3 144cm 2 6.452 0.1550m 2 6.452 × 10 −4 1550in. 3 (cubic inch) ft 3 5.787 × 10 −4 1.728 × 10 3cm 3 16.387 6.102 × 10 −2m 3 1.639 × 10 −5 6.102 × 10 4kg (kilogram) lb (weight) 2.2046 0.4536slug 0.06852 14.594g (gram) 10 3 10 −3kg/m 2 lb/in. 2 (weight) 1.422 × 10 −3 703.0lb/ft 2 (weight) 0.2048 4.882g/cm 2 10 −1 10m (meter) in. (inch) 39.371 2.540 × 10 −2ft (foot) 3.2808 0.30481cm (centimeter) 10 2 10 −2m 2 (square meter) in. 2 1550 6.452 × 10 −4ft 2 10.764 9.290 × 10 −2cm 2 10 4 10 −4m 3 (cubic meter) in. 3 6.102 × 10 4 1.639 × 10 −5ft 3 35.31 2.832 × 10 −2cm 3 10 6 10 −6microbar (dynes/cm 2 ) lb/in. 2 1.4513 × 10 −5 6.890 × 10 4lb/ft 2 2.090 × 10 −3 478.5N/m 2 (Pa) 10 −1 10Np (neper) dB (decibel) 8.686 0.1151N (newton) lb (force) 0.2248 4.448dynes 10 5 10 −5N/m 2 (pascal, Pa) lb/in. 2 (force) 1.4513 × 10 −2 6.890 × 10 3lb/ft 2 (force) 2.090 × 10 −2 47.85dynes/cm 2 10 10 −1lb (force) (pound) N (newton) 4.448 0.2248lb (weight) (pound) slug 0.03108 32.17kg (kilogram) 0.4536 2.2046lb/in. 2 (weight) lb/ft 2 (weight) 144 6.945 × 10 −3kg/m 2 703 1.422 × 10 −3lb/in. 2 (force) lb/ft 2 (force) 144 6.945 × 10 −3N/m 2 (Pa) 6894 1.4506 × 10 −4lb/ft 2 (weight) lb/in. 2 (weight) 6.945 × 10 −3 144g/cm 2 0.4882 2.0482kg/m 2 4.882 0.2048lb/ft 2 (force) lb/in. 2 (force) 6.945 × 10 −3 144N/m 2 (Pa) 47.85 2.090 × 10 −2Slugs lb (weight) 32.17 3.108 × 10 −2kg (kilogram) 14.594 6.852 × 10 −2W (watt) hp (horsepower) 1.341 × 10 −3 745.7
Appendix BBessel FunctionsB.1 The Bessel Differential EquationThe Bessel differential equation of order n, expressed as[x 2 d2dx + x d]2 dx + (x 2 − n 2 ) f (x) = 0carries the solutions consisting of (1) the Bessel functions of the first kind J n (x) forall x, and (2) the Bessel functions of the second kind Y n (x) (also called Neumanfunctions), and the Bessel functions of the third kind H n (1)(2)(x) and H n (x) for all xgreater than zero.B.2 Relationships Between SolutionsH (1)nH (2)n= J n + iY n= J n − iY nJ −n = (−1) n J nY −n = (−1) n Y nB.3 Series Expansions for J 0 and J 1J 0 = 1 − x 22 2 + x 42 2 · 4 2 − x 62 2 · 4 2 · 6 2 +···J 1 = x 2 − 2x 32 · 4 2 + 3x 52 · 4 2 · 6 2 +··· 633
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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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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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Page 589 and 590: 584 19. Sound ReproductionDickason,
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Page 633 and 634: Appendix APhysical Properties of Ma
Page 635: Appendix A. Physical Properties of
Page 639 and 640: B.8 Tables of Bessel Functions, Zer
Page 641 and 642: Appendix CUsing Laplace Transforms
Page 643 and 644: C.3 Solving Differential Equations
Page 645 and 646: C.4 Equations with Multiple-Order R
Page 647 and 648: SolutionC.5 Equations with Complex
Page 649 and 650: C.5 Equations with Complex Roots 64
Page 651 and 652: SolutionC.5 Equations with Complex
Page 653 and 654: 650 IndexAuditoriums, design of, 26
Page 655 and 656: 652 IndexElectrostatic speakers, 58
Page 657 and 658: 654 IndexKey notation, 518Kinetic e
Page 659 and 660: 656 IndexPascal (unit), 48Percent i
Page 661 and 662: 658 IndexSound intensity growth in
Page 663: 660 IndexWater-hammer arresters, 37
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