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

More documents

Recommendations

Info

20.4 Forced Vibration 595Table 20.1. System Response as a Function of Frequency.Frequency Response Controlling Parameterω 2 ≪ ωn 2 x(ω) = F 0kω 2 ≫ ωn 2 x(ω) = F 0mω 2ω 2 = ωn 2 x(ω) = F 0CωStiffness controlledMass controlledDamping controlledratio ξ affects the magnitude of the oscillation peak at resonance and the sharpnessof this resonant peak.In considering the system response as a function of frequency, we observethat the response varies with the frequency as shown in Table 20.1. The relationshipslisted in the table show that each parameter listed—the stiffness, the mass,and damping—effectively controls the response only within a limited region. Forexample, the damping is primarily effective at resonance. The selection of anyvibratory corrective measure depends on whether the excitation frequency is lessthan, greater than, or equal to the resonant frequency of the system.The effect of the amplitude by stiffness, mass, or damping is exemplified by themagnification factor MF, defined asMF = x(ω)F 0 /k = 1√ (20.27)[1 − (ω/ωn ) 2 ] 2 + [2ξ(ω/w n )] 2At resonance ω = ω n , and therefore(MF) resonance = 1(20.28)2ξA measure of the shape of the resonance peak is given by the bandwidth at thehalf-power points, as shown in Figure 20.5. These points are the two points, one tothe right and one to the left of the peak, which have a magnitude equal to (1/ √ 2)of the value of the peak. The square root occurs because power is proportional tothe square of the magnitude.Let us set h ≡ ω n /ω. At half-power points, Equation (20.27) becomes12 √ 2ξ = 1√(1 − h2 ) 2 + (2ξh) 2Solving the preceding equation algebraically for h 2 results inh 2 = 1 − 2ξ ± 2ξ √ 1 + ξ 2We also assume small values of damping (i.e., ξ ≪ 1) and neglect second-orderterms. Then the following result occurs:h 2 = 1 ± 2ξ
596 20. Vibration and Vibration ControlFigure 20.5. Principal features of a resonance peak.ThenHenceWe approximateh 1 =( ωω n) 2= 1 − 2ξ, h 2 =( ωω n) 2= 1 + 2ξThe bandwidth bw is given byω 2 2 − ω2 1ω 2 nh 2 − h 1 = 4ξbw = (ω 2 − ω 1 )ω n≈ 2(ω 2 − ω 1 )ω n= ωω= 2ξ (20.29)The reciprocal of the bandwidth is the quality factor Q, expressed asQ = ω nω = 1(20.30)2ξWhen a frequency response of system is plotted in the format of Figure 20.5,this figure in conjunction with Equation (20.30) can provide the basis for findingthe equivalent viscous damping of the system.
Page 2:
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:
Page 19:
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 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62:
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
Page 105 and 106:
96 5. Vibrating Barsthe acceleratio
Page 107 and 108:
98 5. Vibrating BarsFigure 5.5. Loc
Page 109 and 110:
100 5. Vibrating Barsmore difficult
Page 111 and 112:
102 5. Vibrating BarsFigure 5.7. An
Page 113 and 114:
104 5. Vibrating Barsthe light beam
Page 115 and 116:
106 5. Vibrating BarsFigure 5.8. Tr
Page 117 and 118:
108 5. Vibrating BarsFigure 5.10. T
Page 119 and 120:
110 5. Vibrating Barsof 0.005 m dia
Page 121 and 122:
112 6. Membrane and PlatesFigure 6.
Page 123 and 124:
114 6. Membrane and PlatesBecause t
Page 125 and 126:
116 6. Membrane and PlatesThe left-
Page 127 and 128:
118 6. Membrane and PlatesTable 6.1
Page 129 and 130:
120 6. Membrane and PlatesIn real a
Page 131 and 132:
122 6. Membrane and PlatesTable 6.2
Page 133 and 134:
124 6. Membrane and PlatesAt low fr
Page 135 and 136:
126 6. Membrane and PlatesThe elast
Page 137 and 138:
128 6. Membrane and PlatesFor the f
Page 139 and 140:
130 6. Membrane and Plates(b) Deter
Page 141 and 142:
132 7. Pipes, Waveguides, and Reson
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
152 8. Acoustic Analogs, Ducts, and
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
9Sound-Measuring Instrumentation9.1
Page 183 and 184:
9.3 Microphones 175Figure 9.1. A cu
Page 185 and 186:
SolutionEquation (9.3) is applied t
Page 187 and 188:
9.5 Selection and Positioning of Mi
Page 189 and 190:
9.6 Vector Sound Intensity Probes 1
Page 191 and 192:
9.8 Proper Procedures for Using the
Page 193 and 194:
9.8 Proper Procedures for Using the
Page 195 and 196:
Example Problem 39.10 Dosimeters 18
Page 197 and 198:
9.11 Noise Measurement in Selected
Page 199 and 200:
9.11 Noise Measurement in Selected
Page 201 and 202:
9.12 Real Time Analysis 193analyzer
Page 203 and 204:
9.13 Fast Fourier Transform Analysi
Page 205 and 206:
9.14 Data Windows and Selection of
Page 207 and 208:
9.16 Measurement Error 199whereβ =
Page 209 and 210:
9.18 Measurement of Sound in a Free
Page 211 and 212:
9.20 Sound Power Measurement in a D
Page 213 and 214:
9.20 Sound Power Measurement in a D
Page 215 and 216:
9.23 The Addition Method for Measur
Page 217 and 218:
References 209acoustical output and
Page 219 and 220:
Problems for Chapter 9 2112. Determ
Page 221 and 222:
214 10. Physiology of Hearing and P
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
Page 249 and 250:
11Acoustics of Enclosed Spaces:Arch
Page 251 and 252:
11.2 Sound Fields 245Figure 11.1. P
Page 253 and 254:
11.4 Sound Intensity Growth in a Li
Page 255 and 256:
11.5 Sound Absorption Coefficients
Page 257 and 258:
11.6 Growth of Sound with Absorbent
Page 259 and 260:
11.7 Decay of Sound 253Following Sa
Page 261 and 262:
11.8 Decay of Sound in Dead Rooms 2
Page 263 and 264:
11.9 Reverberation as Affected by S
Page 265 and 266:
11.13 Sound Levels due to Direct an
Page 267 and 268:
11.15 Concert Halls and Opera House
Page 269 and 270:
Figure 11.9. A view of the Boston S
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
11.16 Band Shells and Outdoor Audit
Page 279 and 280:
11.16 Band Shells and Outdoor Audit
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
Page 293 and 294:
12.6 Coincidence Effect and Critica
Page 295 and 296:
12.7 The Double-Panel Partition 289
Page 297 and 298:
an ideal gas) varies in the followi
Page 299 and 300:
12.8 Measuring Transmission Loss 29
Page 301 and 302:
12.10 Combined Sound Transmission C
Page 303 and 304:
12.11 Noise Insulation Ratings 297F
Page 305 and 306:
12.11 Noise Insulation Ratings 299s
Page 307 and 308:
12.12 Noise Reduction of a Wall 301
Page 309 and 310:
12.12 Noise Reduction of a Wall 303
Page 311 and 312:
12.14 Enclosures 305to the extent t
Page 313 and 314:
12.14 Enclosures 307and similarly f
Page 315 and 316:
12.15 Small Enclosures 309walls. Ac
Page 317 and 318:
12.16 Acoustic Barriers 311Figure 1
Page 319 and 320:
12.16 Acoustic Barriers 313In the c
Page 321 and 322:
Equation (12.67) becomes(11D = λ+
Page 323 and 324:
Problems for Chapter 12 3173. A 0.7
Page 325 and 326:
13Criteria and Regulations forNoise
Page 327 and 328:
13.3 The Occupational Safety and He
Page 329 and 330:
13.4 Perception of Noise 323inspect
Page 331 and 332:
13.6 Indoor Noise Criteria 325accou
Page 333 and 334:
13.6 Indoor Noise Criteria 327Room
Page 335 and 336:
13.7 Equivalent Sound Level, Day-Ni
Page 337 and 338:
13.7 Equivalent Sound Level, Day-Ni
Page 339 and 340:
Composite Noise Rating13.9 Rating o
Page 341 and 342:
13.10 Evaluation of Traffic Noise 3
Page 343 and 344:
Page 345 and 346:
Highway Construction Noise13.10 Eva
Page 347 and 348:
Page 349 and 350:
Page 351 and 352:
13.11 Evaluation of Community Noise
Page 353 and 354:
13.12 Guidelines and Regulations in
Page 355 and 356:
Page 357 and 358:
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
Page 365 and 366:
14.4 Fan or Blower Noise 359Table 1
Page 367 and 368:
14.4 Fan or Blower Noise 361Figure
Page 369 and 370:
Page 371 and 372:
Page 373 and 374:
14.6 Pumps and Plumbing Systems 367
Page 375 and 376:
14.6 Pumps and Plumbing Systems 369
Page 377 and 378:
14.8 Gears 371fromwheref BRC = N r
Page 379 and 380:
14.8 Gears 373Figure 14.7. Gear noi
Page 381 and 382:
14.8 Gears 375Figure 14.8. Gear tra
Page 383 and 384:
14.8 Gears 377The subscripts 1 and
Page 385 and 386:
14.10 Ball and Roller Bearings 379l
Page 387 and 388:
14.10 Ball and Roller Bearings 381c
Page 389 and 390:
14.11 Other Mechanical Drive Elemen
Page 391 and 392:
Belt Drivesf CL = n 1N 1 2400 × 12
Page 393 and 394:
14.12 Gas-Jet Noise 387said to be c
Page 395 and 396:
14.12 Gas-Jet Noise 389power discha
Page 397 and 398:
Solution14.12 Gas-Jet Noise 391Usin
Page 399 and 400:
14.13 Gas Jet Noise Control 393Solu
Page 401 and 402:
14.13 Gas Jet Noise Control 395Figu
Page 403 and 404:
14.13 Gas Jet Noise Control 397Figu
Page 405 and 406:
14.14 Mufflers and Silencers 399Fig
Page 407 and 408:
(1 + m)A I 1=A 314.14 Mufflers and
Page 409 and 410:
14.14 Mufflers and Silencers 403Let
Page 411 and 412:
References 405Figure 14.21 illustra
Page 413 and 414:
Problems for Chapter 14 407the nois
Page 415 and 416:
15Underwater Acoustics15.1 Sound Pr
Page 417 and 418:
15.3 Speed of Sound in Seawater 411
Page 419 and 420:
15.4 Velocity Profiles in the Sea 4
Page 421 and 422:
15.4 Velocity Profiles in the Sea 4
Page 423 and 424:
15.5 Underwater Transmission Loss 4
Page 425 and 426:
15.6 Parametric Variation of Absorp
Page 427 and 428:
15.8 Underwater Refraction 421Figur
Page 429 and 430:
15.9 Mixed Layer 423When G is const
Page 431 and 432:
15.11 Sonar Transducers and Their P
Page 433 and 434:
Example Problem 115.12 The Sonar Eq
Page 435 and 436:
Active and Passive Equations15.12 T
Page 437 and 438:
15.13 Noise, Echo, and Reverberatio
Page 439 and 440:
15.13 Noise, Echo, and Reverberatio
Page 441 and 442:
15.14 Transient Form of Sonar Equat
Page 443 and 444:
Example Problem 315.16 Shortcomings
Page 445 and 446:
15.17 Theoretical Target Strength o
Page 447 and 448:
Problems for Chapter 15 441Wilson,
Page 449 and 450:
444 16. Ultrasonicscatching small i
Page 451 and 452:
446 16. UltrasonicsPlanck constant
Page 453 and 454:
448 16. UltrasonicsEquation (16.5)
Page 455 and 456:
450 16. UltrasonicsFigure 16.1. Sou
Page 457 and 458:
452 16. Ultrasonicsthe positive hal
Page 459 and 460:
454 16. Ultrasonicson each and ever
Page 461 and 462:
456 16. Ultrasonicscomplete as a li
Page 463 and 464:
458 16. Ultrasonicsinitial of their
Page 465 and 466:
460 16. Ultrasonicsoptic axis, deno
Page 467 and 468:
462 16. Ultrasonicstransducer, it h
Page 469 and 470:
464 16. UltrasonicsTable 16.1. Valu
Page 471 and 472:
466 16. Ultrasonicsthe mechanical r
Page 473 and 474:
468 16. UltrasonicsThe Physics of M
Page 475 and 476:
470 16. UltrasonicsFigure 16.7. The
Page 477 and 478:
472 16. Ultrasonicscurvilinear arra
Page 479 and 480:
474 16. Ultrasonics(a)amplitudeinpu
Page 481 and 482:
476 16. Ultrasonicsslow to allow th
Page 483 and 484:
478 16. Ultrasonics5. In the cases
Page 485 and 486:
480 17. Commercial and Medical Ultr
Page 487 and 488:
Page 489 and 490:
Page 491 and 492:
Page 493 and 494:
Page 495 and 496:
Page 497 and 498:
Page 499 and 500:
Page 501 and 502:
Page 503 and 504:
Page 505 and 506:
Page 507 and 508:
Page 509 and 510:
Page 511 and 512:
Page 513 and 514:
Page 515 and 516:
510 18. Music and Musical Instrumen
Page 517 and 518:
Page 519 and 520:
Figure 18.7. The frequencies of the
Page 521 and 522:
Page 523 and 524:
Page 525 and 526:
Page 527 and 528:
Page 529 and 530:
Page 531 and 532:
Page 533 and 534:
Page 535 and 536:
Page 537 and 538:
Page 539 and 540:
Figure 18.20. The violin octet deve
Page 541 and 542:
Page 543 and 544:
Page 545 and 546:
Page 547 and 548:
Page 549 and 550: 544 18. Music and Musical Instrumen
Page 575 and 576: 570 19. Sound ReproductionAlbert, a
Page 577 and 578: 572 19. Sound ReproductionD. Magnet
Page 579 and 580: 574 19. Sound Reproductionon, machi
Page 581 and 582: 576 19. Sound ReproductionIt is fai
Page 583 and 584: 578 19. Sound ReproductionINNER SUS
Page 585 and 586: 580 19. Sound Reproductiontuned ape
Page 587 and 588: 582 19. Sound Reproductionuse of MP
Page 589 and 590: 584 19. Sound ReproductionDickason,
Page 591 and 592: 586 20. Vibration and Vibration Con
Page 599: 594 20. Vibration and Vibration Con
Page 623 and 624: 618 21. Nonlinear Acousticsby∇ 2
Page 625 and 626: 620 21. Nonlinear Acousticsmay be i
Page 627 and 628: 622 21. Nonlinear Acousticswhereδ
Page 629 and 630: 624 21. Nonlinear AcousticsThe shoc
Page 631 and 632: 626 21. Nonlinear AcousticsBut the
Page 633 and 634: Appendix APhysical Properties of Ma
Page 635 and 636: Appendix A. Physical Properties of
Page 637 and 638: Appendix BBessel FunctionsB.1 The B
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
show all

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

Create successful ePaper yourself

Delete template?

Save as template?