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

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68 3. Sound Wave Propagation and CharacteristicsProblems for Chapter 31. A signal consists of the following components:y 1 = 10 sin 4t, y 2 = 6 sin 8t, y 3 = 4.3 sin 10tPlot each component and add them up to obtain a composite wave.2. A 300-Hz sound wave is propagating axially in a steel bar. Find the wavelengthand the wave number.3. Determine the wave number and the wavelength of a 30-Hz pure tone at20 ◦ C.4. Two sine waves have approximately the same amplitudes, but one is at afrequency of 135.3 Hz and the other 136.0 Hz. What is the beat frequency?What is the time duration between the beats?5. Show mathematically how noise cancellation can be effected by duplicatingan offending signal and changing its phasing. In real life situation, can thecancellation be a total one? If not, why not?6. It is desired to place a worker at a “quieter” location near a machine that putsout a steady 400 Hz hum. Where would this location be and where are thepoints where the noise would be greater?7. A train whistle is measured with its frequency at 250 Hz when the trainsapproaches the observer near the tracks at the rate of 125 km/h. Predict thefrequency when the train is pulling away from the observer.8. Train A traveling 60 km/h is approaching Train B traveling on a parallel trackat 85 km/h. Train A blows its whistle which has a fundamental of 255 Hz. Whatfrequency will the engine man at Train B hear? What will be the perceivedfrequency after the whistle on Train B passes the locomotive of Train A?Neglect the distance between the tracks.9. An observer stands 150 km from a railroad track. A train is 300 km on thenormal from the track to the observer. It is traveling at 80 km/h and approachingthis normal. Its whistle emits a fundamental of 300 Hz. What will be thefrequency of this signal perceived by the observer?10. Develop an equation for the rate of change of the frequency with respect toan observer subtending an angle θ with a source’s direction. The source ismoving at a velocity V .11. A boundary exists between two mediums, A and B, through which an acousticsignal travels. The signal traveling in Medium A impinges the boundary atan angle of 45 ◦ . In passing into Medium B on the other side of the boundarythe signal refracts at an angle of 55 ◦ . The velocity of sound in Medium A is450 m/s. Determine the velocity of sound in Medium B on the other side ofthe boundary.12. Given a 150-Hz signal expressed asp(x, t) = 35 sin 2.5(x − 344t)determine the followings:
Problems for Chapter 3 69(a) the wave number(b) the wavelength(c) the root-mean-square pressure13. Convert the following rms pressures into decibels:(a) 20 μPa(b) 150 μPa(c) 1 kPa(d) 50 kPa14. Convert the following values expressed in dB into rms pressure:(a) 20 dB(b) 60 dB(c) 90 dB(d) 130 dB15. Two machines are running. One machine puts out 95 dB and the other 98 dB.What will be the combined sound pressure level in dB?16. Three machines are operating simultaneously. Their combined noise level is115 dB. One machine is shut down and noise level drops to 110 dB. Theremaining two machines have identical noise output. What is the noise outputof these two machines?17. An octave-band analysis of a machine yields the following results:Band-center frequencySPL (Hz)31.5 7263 76125 77250 72500 691000 842000 924000 838000 8016,000 78Find the total A-weighted sound level, the total B-weighted sound level, andthe total C-weighted sound level.18. The following SPL readings were taken of a noisy electric generator:Amount of time, sUnweighted SPL reading, dB15 73.422 79.420 88.912 91.9Find the equivalent sound pressure level L eq .
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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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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
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Page 65 and 66: 3.14 Performance Indices for Enviro
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Page 73 and 74: 3.18 The Monopole Source 63The thre
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Page 77: References 67medium. The time avera
Page 81 and 82: 4Vibrating Strings4.1 IntroductionI
Page 83 and 84: 4.4 General Solution of the Wave Eq
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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
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Page 113 and 114: 104 5. Vibrating Barsthe light beam
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Page 117 and 118: 108 5. Vibrating BarsFigure 5.10. T
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Page 121 and 122: 112 6. Membrane and PlatesFigure 6.
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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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