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

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266 11. Acoustics of Enclosed Spaces: Architectural AcousticsFigure 11.12. Transmission of sound to all areas of an auditorium through the ceiling andfloor profiling.shown how a ceiling can convey sound to the listeners without imposing a greattime difference between direct and ceiling-reflected sound. Floor profile is alsoimportant in establishing the proper ratio of direct to indirect sound. Splays on theside walls have proven effective in promoting diffusion and uniformity of loudness.Rear walls generally should be absorbent to minimize echoes being sent back tothe stage.Many concert halls have been built throughout the world, some with outstandingacoustics and others resulting in dismal sound. Among the features common to allof the aurally superior halls are a limited audience capacity (generally 2800 seatsor less), extreme clarity of sound so that the audience can clearly distinguished theindividual instruments of the orchestra without loss of fullness or blending of tonesassociated with reverberation. A good hall also allows the orchestra to hear itself.Table 11.2 contains a summary of the characteristics of a number of prominentmusical facilities all over the world. Figure 11.13 shows the stage view ofthe Orchestra Hall in Minneapolis (1974), which is patterned after the classicalrectangular design. The hall contains a slanted floor with 1590 seats and an additional983 seats are located in the three-stepped balcony tiers, making for a totalaudience capacity of 2573. A random pattern of plaster cubes covers the ceiling,providing effective diffusion of sound throughout the hall. This overlay of cubesalso continues down the back wall, behind the stage, as shown in Figure 11.13.Wood paneling partially covers the walls, and both the flooring of the stage andaudience areas are wood. This concert hall is notable for its clarity, dynamic range,and balance.Another acoustic success among the contemporary musical facilities is theKennedy Center for the Performing Arts which opened in Washington, D.C. in1971. The Center consists of a single structure that contains a 2759-seat concerthall, a 2319-seat opera house (Figure 11.14), and a 1142-seat theater. The locationwas environmentally challenging, for the Center is situated on a site near thePotomac River, in close proximity to the Washington Ronald Reagan NationalAirport on the other side of the river. Both commercial and private aircraft fly as
11.15 Concert Halls and Opera Houses 267Table 11.2. Reverberation Times of Leading Concert Halls and Auditoriums.Reverberation Time aVolume (ft 3 ) Seating Capacity Occupied UnoccupiedUnited StatesBaltimore, lyric Theatre 744,000 2616 1.47 2.02Boston Symphony Hall 662,000 2631 1.8 2.77Buffalo, Kleinhans Music Hall 644,000 2839 1.32 1.65Cambridge, Kresge Auditorium 354,000 1238 1.47 1.7Chicago, Aric Crown Theatre 1,291,000 5081 1.7 2.45Cleveland, Severance Hall 554,000 1890 1.7 1.9Detroit, Ford Auditorium 676,000 2926 1.55 1.95New York, Carnegie Hall 857,000 2760 1.7 2.15Philadelphia Academy of Music 555,000 2984 1.4 1.55Purdue University Hall of Music 1,320,000 6107 1.45 1.6Rochester, New York, Eastman Theatre 900,000 3347 1.65 1.82AustriaVienna, Grosser Musikvereinssaal 530,000 1680 2.05 3.6BelgiumBrussels, Palais des Beaux-Arts 442,000 2150 1.42 1.95CanadaEdmonton and Calgary, Alberta Jubilee Halls 759,000 2731 1.42 1.8Vancouver, Queen Elizabeth Theatre 592,000 2800 1.5 1.9DenmarkTivoli Koncertsal 450,000 1789 1.3 2.25FinlandTurku, Konserttisali 340,000 1002 1.6 1.95GermanyBerlin, Musikhochschule Konzertsaal 340,000 1340 1.65 1.95Bonn, Beethovenhalle 555,340 1407 1.7 1.95Great BritainEdinburgh, Usher Hall 565,000 2760 1.65 2.52Liverpool Philharmonic Hall 479,000 1955 1.5 1.65London, Royal Albert Hall 3,060,000 5080 2.5 3.7London, Royal Festival Hall 755,000 3000 1.47 1.77IsraelTel Aviv, Frederic R. Mann Auditorium 750,000 2715 1.55 1.97ItalyMilan, Teatro Alla Scala 397,300 2289 1.2 1.35NetherlandsAmsterdam, Concertgebouw 663,000 2206 2.0 2.4SwedenGothenburg, Konserthus 420,000 1371 1.7 2.0SwitzerlandZurich, Grosser Tonhallesaal 402,500 1546 1.6 3.85VenezuelaCaracas, Aula Magna 880,000 2660 1.35 1.8a At 500–1000 Hz.
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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
Page 221 and 222: 214 10. Physiology of Hearing and P
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Page 251 and 252: 11.2 Sound Fields 245Figure 11.1. P
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Page 259 and 260: 11.7 Decay of Sound 253Following Sa
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Page 263 and 264: 11.9 Reverberation as Affected by S
Page 265 and 266: 11.13 Sound Levels due to Direct an
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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
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Page 295 and 296: 12.7 The Double-Panel Partition 289
Page 297 and 298: an ideal gas) varies in the followi
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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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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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