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

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364 14. Machinery Noise Control1 kPa (4.0 in. water gauge). Table 14.2 lists the relative sound power for a varietyof fan types. In reducing all fan noise data to this common base, the concept ofspecific sound power level allows direct comparison to be made between the octaveband levels of different types of fans. A blade frequency increment (BFI) is alsolisted in Table 14.2; this represents the number of decibels that must be added tothe level of the octave band, which includes the blade frequency in order to accountfor the presence of such a tone. Also, a means is provided for estimating the noiselevel of fans under actual operating conditions by a procedure that consists of thefollowing steps:1. Select the fan type and obtain the specific power levels in octave bands fromTable 14.2. These sound power levels are expressed in decibels re 1 pW.2. Adjust the octave-band levels for the volume flow rate and the operating pressureby adding to each octave band one of the following values:orwhere10 log Q + 20 log p t dB (for metric units) (14.3a)10 log Q + 20 log p t − 45 dB (for English units) (14.3b)Q = volume flow rate, m 3 /s or cfmp t = total pressure, kPa or inches water gauge3. Account for the blade frequency component of the fan by adding the BFI forthe fan type chosen to the octave-band level of that band which includes theblade frequency. The blade frequency is found from the use of Equation (14.2).4. The sum of the above equals the total sound power level of the radiation fromthe inlet and the outlet. Subtract 3 dB from each octave band to yield the soundpower level of radiation from the inlet or the outlet.Example Problem 2Consider a radial forward-curved fan with 24 blades, having a rotor diameter of0.8 m, and operating at 750 rpm with a volume flow rate of 18 m 3 /s and with atotal pressure of 1.5 kPa.Find the total sound output power at the inlet.SolutionWe use Table 14.2 and list the calculations at each step for each octave band levelin Table 14.3. For step 2, using Equation (14.3a)10 log Q + 20 log p t = 10 log 18 + 20 log 1.5 = 16
14.4 Fan or Blower Noise 365Table 14.3. Calculation Results for Sound Power Level.Octave-Band Center Frequencies, HzProcedural Step 63 125 250 500 1000 2000 4000 80001 98 98 88 81 81 76 71 662 16 16 16 16 16 16 16 163 0 0 2 0 0 0 0 04 −3 −3 −3 −3 −3 −3 −3 −3Radiation form inlet 111 111 103 94 94 89 84 79The blade frequency is from Equation (14.2)f B = nN60=750 × 2460= 300 Hzwhich lies in the octave band with the center frequency of 250 Hz. The BFI is 2 dB.Step 3 is now completed. Step 4 consists of subtracting 3 dB from each octaveband to obtain the noise from the inlet alone.Fan LawsFan laws can predict fan performance quite well over a wide range of size andspeed. These laws are as follows:( ) 3 ( )da naQ a = Q b (14.4)d b n bp ta = p tb(dad b) 2 (nan b) 2(14.5)where( ) 5 ( ) 3 da naP a = P b (14.6)d b n b( ) ( )danaL wa = L Wb + 70 log + 50 log(14.7)d b n bQ = volume flow rate, m 3 /sp t = total pressure, kPaP = fanpower,kWL W = sound power level, dB re 1 pWd = rotor diameter, mn = rotor speed, rpmSubscript a denotes the parameters for the base curve performance conditions, andsubscript b denotes the parameters for the desired performance conditions.
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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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Page 323 and 324: Problems for Chapter 12 3173. A 0.7
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Page 359 and 360: References 353Computer Program, HIC
Page 361 and 362: Problems for Chapter 13 355Problems
Page 363 and 364: 14Machinery Noise Control14.1 Intro
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Page 381 and 382: 14.8 Gears 375Figure 14.8. Gear tra
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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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