Acoustics: Sound Fields, Transducers and Vibration, Second Edition guides readers through the basics of sound fields, the laws governing sound generation, radiation, and propagation, and general terminology. Specific sections cover microphones (electromagnetic, electrostatic, and ribbon), earphones, and horns, loudspeaker enclosures, baffles and transmission lines, miniature applications (e.g. MEMS microphones and micro speakers in tablets and smart phones), sound in enclosures of all sizes, such as school rooms, offices, auditoriums and living rooms, and fluid-structure interaction. Numerical examples and summary charts are given throughout the text to make the material easily applicable to practical design.
New to this edition:
A chapter on electrostatic loudspeakers
A chapter on vibrating surfaces (membranes, plates, and shells)
Readers will find this to be a valuable resource for experimenters, acoustical consultants, and to those who anticipate being engineering designers of audio equipment. It will serve as both a text for students in engineering departments and as a valuable reference for practicing engineers.
Provides detailed acoustic fundamentals, enabling better understanding of complex design parameters, measurement methods and data
Extensive appendices cover frequency-response shapes for loudspeakers, mathematical formulas and conversion factors
Author(s): Leo Beranek, Tim Mellow
Edition: 2
Publisher: Academic Press
Year: 2019
Language: English
Pages: 879
Cover......Page 1
Cover Details......Page 2
APPENDIX
I - Frequency response shapes for loudspeakers [1]......Page 3
Copyright......Page 4
Preface to the second edition......Page 5
Preface to the first edition......Page 6
Acknowledgments......Page 8
1.1 A little history......Page 9
1.2 What is sound?......Page 13
1.3 Propagation of sound through gas......Page 16
1.4 Measurable aspects of sound......Page 18
Acoustic......Page 19
Harmonically varying quantity......Page 20
Root mean square value......Page 21
Static pressure (P0)......Page 22
Speed of sound (c)......Page 23
Specific acoustic impedance (Zs)......Page 24
Sound energy density (D)......Page 25
Electric power level or acoustic intensity level......Page 26
Intensity level (IL)......Page 27
Acoustic power level (PWL)......Page 28
Sound level......Page 29
Pressure spectrum level......Page 30
Notes......Page 31
13.2 The Rayleigh integrals and Green's function......Page 32
Air-suspension loudspeaker system......Page 335
2.2.2 The gas law......Page 35
Resultant field......Page 557
High frequencies......Page 473
2.2.6 The wave equation in spherical coordinates......Page 40
2.2.7 General one-dimensional wave equation (Webster's equation) [6]......Page 41
2.3 General solutions of the one-dimensional wave equation......Page 42
2.3.1 General solution......Page 43
2.3.2 Steady-state solution......Page 44
2.4 Solution of wave equation for air in a tube terminated by an impedance......Page 50
Particle velocity......Page 51
Transmitted and reflected pressures......Page 52
Impedance......Page 53
Impedance measurement......Page 54
Rigid termination (infinite impedance)......Page 55
Sound pressure......Page 58
Specific acoustic impedance......Page 60
Solution of the inhomogeneous wave equation for a closed tube......Page 62
Far-field pressure......Page 586
Expansions for cot and csc......Page 64
Solution of the inhomogeneous wave equation for an open tube......Page 65
Impedance of the open tube......Page 66
12.10 Radiation from an oscillating concave dome in an infinite baffle......Page 595
2.7 Solution of wave equation for air in a tube filled with absorbent material......Page 67
Specific acoustic impedance......Page 68
Sound pressure......Page 69
Particle velocity......Page 70
Far-field response of the induction loudspeaker......Page 781
Sound pressure......Page 72
Specific acoustic impedance......Page 73
15.10 Electro-mechano-acoustical circuit......Page 75
The plane wave equation in z......Page 76
2.12 Cylindrical coordinates......Page 77
The radial equation in w......Page 78
The azimuthal equation in φ......Page 79
2.13 Spherical coordinates......Page 80
The radial equation in r......Page 82
The inclination equation in θ......Page 83
The azimuth equation in φ......Page 84
Notes......Page 85
Part VI: Mechanical circuits......Page 87
Pressure field......Page 554
3.2 Physical and mathematical meanings of circuit elements......Page 88
3.3 Mechanical elements......Page 91
Voice-coil velocity at low frequencies......Page 94
Mechanical compliance CM......Page 95
Mechanical resistance RM and mechanical conductance GM......Page 97
Theoretical considerations......Page 479
Simple lever......Page 100
Floating lever......Page 101
3.4 Acoustical elements......Page 108
4.7 Perforated sheet—mixed mass-resistance element [a (in meters)﹥0.01/f and a<10/f] [3,4]......Page 159
Acoustic compliance CA......Page 111
Acoustic resistance RA and acoustic conductance GA......Page 112
Acoustic generators......Page 113
Mechanical rotational systems......Page 118
Electromagnetic-mechanical transducer......Page 119
12.6 Radiation from a spherical cap in a sphere......Page 571
Far-field pressure......Page 121
3.6 Mechanoacoustic transducer......Page 126
3.7 Examples of transducer calculations......Page 127
3.8 Conversion from admittance-type analogies to impedance-type analogies......Page 130
3.9 Thévenin's theorem......Page 131
3.10 Transducer impedances......Page 133
Near-field pressure......Page 654
Transmission matrix for an electromagnetic-mechanical transducer......Page 134
Impedance matrix for an electromagnetic-mechanical transducer......Page 137
Transmission matrix for an electrostatic-mechanical transducer......Page 139
Impedance matrix for an electrostatic-mechanical transducer......Page 141
Analogous circuits for the two-port network using z-parameters [12]......Page 142
Notes......Page 146
4.1 Introduction......Page 148
10.1 Introduction......Page 149
4.3 Acoustic compliances......Page 150
Series acoustic compliance......Page 151
4.4 Acoustic resistances......Page 154
Narrow slit [2] [t (in meters)<0.003/f]......Page 156
10.5 Examples of rectangular enclosures......Page 157
15.5 Effect of discretization into rings of finite width......Page 800
Medium tube [a (in meters)﹥0.01/f and a <10/f] [3,4]......Page 158
Protection against damage to the loudspeaker......Page 160
Boundary condition of zero radial strain at the perimeter......Page 754
Part XI: Elementary reflection and radiation of sound......Page 166
9.9 Infinite parabolic horn [11]......Page 167
Radiation impedance......Page 171
15.11 Negative compliance and stability......Page 173
Linear array of point sources......Page 176
4.13 Steered beam-forming array of point sources......Page 178
4.14 Dipole point source (doublet)......Page 184
Near-field and far-field......Page 188
4.15 Radiation from an oscillating sphere......Page 189
Near-field pressure......Page 190
Far-field pressure......Page 191
Radiation impedance......Page 193
4.16 Directivity index and directivity factor......Page 194
Calculation of Q(f) and DI(f)......Page 195
4.18 Oscillating sphere......Page 201
4.19 Plane circular piston in infinite baffle......Page 203
Approximate analogous circuits......Page 204
Low- and high-frequency approximations......Page 206
4.20 Plane circular free disk......Page 207
4.21 Plane circular piston radiating from one side only in free space......Page 208
4.22 Sound in lossy tubes......Page 212
Categories......Page 213
Thermal conduction (entropy) and the gas law......Page 214
Solution of the velocity and temperature radial equations......Page 215
Mass conservation and Helmholtz wave equation......Page 218
Dynamic compressibility......Page 219
A two-port network for a finite tube of any length [13]......Page 220
A two-port network for a short finite tube......Page 222
A two-port network for a short finite tube using approximate discrete elements......Page 223
Regimes for an open-ended tube......Page 226
Ultra-narrow tube......Page 230
References......Page 234
Part XV: General characteristics of microphones......Page 235
5.1 Pressure microphones......Page 236
5.2 Pressure-gradient microphones......Page 237
5.3 Combination of pressure and pressure-gradient microphones......Page 241
14.5 Green's function for a rectangular membrane......Page 723
Electro-mechano-acoustical relations......Page 245
Voice-coil velocity at medium and low frequencies......Page 286
Performance......Page 249
6.6 Sound pressure produced at distance r......Page 252
Construction......Page 253
Electromechanical relations......Page 255
Analogous circuits......Page 257
Far-field pressure......Page 259
Performance......Page 260
6.7 Frequency–response curves......Page 295
15.8 Neutralization of stray capacitances......Page 808
Outline placeholder......Page 0
Construction......Page 263
Measurement of VAS......Page 302
Far-field pressure......Page 574
5.7 Electrical combination of pressure and pressure-gradient transducers......Page 266
5.9 Dual-diaphragm combination of pressure and pressure-gradient microphones......Page 269
Throat impedance......Page 488
Bidirectional performance......Page 276
Loudness rating......Page 460
Condition for stability......Page 278
Notes......Page 279
Six. Electrodynamic loudspeakers......Page 280
Reference......Page 834
13.1 The Huygens–Fresnel principles......Page 605
6.2 Construction [2]......Page 281
6.3 Electro-mechano-acoustical circuit......Page 283
9.4 Frequency response......Page 470
6.5 Thiele–Small parameters [5]......Page 291
Loudness of the bass sounds......Page 526
6.8 Electrical input impedance......Page 297
At resonance......Page 298
Envelopment......Page 299
6.10 Measurement of Thiele–Small parameters......Page 300
Measurement of RE......Page 301
Far-field pressure......Page 569
6.11 Examples of loudspeaker calculations......Page 304
Part XX: design factors affecting direct-radiator loudspeaker performance......Page 305
6.12 Magnet size......Page 306
Effect of coil size on efficiency......Page 310
Number of turns and wire diameter......Page 312
9.14 Bends in horns......Page 313
Directivity patterns for typical loudspeakers......Page 317
Diaphragm volume velocity U˜c......Page 363
Intensity level on designated axis......Page 318
6.16 Transfer functions and the Laplace transform......Page 319
6.17 Transient response......Page 321
Suspension compliance......Page 326
Force factor......Page 327
Coil inductance......Page 328
Cone displacement......Page 368
Doppler effect......Page 330
References......Page 333
Part XXI: Simple enclosures......Page 334
Transmission-line enclosures......Page 336
7.2 Unbaffled direct-radiator loudspeaker......Page 337
7.4 Finite-sized flat baffle......Page 339
7.6 Closed-box baffle [2,3]......Page 340
Analogous circuit......Page 344
Far-field pressure......Page 345
Impedance of closed box with absorbent lining......Page 347
Sound propagation in homogeneous absorbent materials [5]......Page 350
Impedance of closed box with or without absorbent lining at all frequencies......Page 352
Unlined closed box at low frequencies......Page 355
Location of loudspeaker drive unit in box......Page 356
Effect of box compliance on resonance frequency and Q......Page 357
Values of radiation (front-side) impedance......Page 358
Small- to medium-sized box (less than 200L)......Page 359
Radiation equation......Page 360
Reference volume velocity and sound pressure......Page 364
Alignments for predetermined frequency-response shapes......Page 365
Setting the value of QTC and determination of the total box volume VT......Page 367
15.6 A practical delay line......Page 369
Final set of simultaneous equations for the power-series coefficients......Page 763
7.8 General description......Page 377
7.9 Acoustical circuit......Page 379
13.10 Radiation from a rigid circular piston in a finite circular open baffle [26,27]......Page 380
7.11 Radiated sound......Page 384
7.12 Alignments for predetermined frequency-response shapes......Page 385
7.13 Port dimensions......Page 389
13.13 The Bouwkamp impedance theorem [36]......Page 390
7.15 Electrical input impedance and evaluation of QL......Page 391
7.17 Construction and adjustment notes......Page 393
7.18 Two-port network for a bass-reflex enclosure......Page 405
General description......Page 412
Acoustical circuit......Page 415
Electromechanoacoustical circuit......Page 416
Radiated sound......Page 417
Performance......Page 419
7.20 Crossover filters......Page 428
Classical crossover filters......Page 429
High-pass crossover filters which take into account the native response of the tweeter......Page 430
Third-order high-pass filter with a series capacitor......Page 431
Fourth-order high-pass filter with a series capacitor and shunt inductor......Page 435
Effect of phase delay of second-order crossover on time-domain response to square waves......Page 438
Crossover filters with zero phase shift......Page 439
7.21 Dual-concentric drive units......Page 443
References......Page 444
Wave equation for the membrane in free space......Page 447
References......Page 854
Microphone......Page 448
8.2 Circuit diagram for a cell phone loudspeaker/receiver......Page 449
Acoustic low-pass filter (helmholtz resonator)......Page 450
Dust screens......Page 451
Turbulence......Page 452
8.4 Head and torso simulator......Page 453
Electret microphones......Page 454
Microelectromechanical system microphones......Page 457
8.6 Measurements for type approval......Page 459
Sidetone......Page 462
References......Page 464
9.1 Introduction......Page 465
15.1 Introduction to electrostatic loudspeakers......Page 789
9.2 Electro-mechano-acoustical circuit [1]......Page 466
9.3 Reference efficiency......Page 468
Low frequencies......Page 471
12.4 Scattering from a rigid sphere by a point source......Page 561
9.7 Possible profiles [2]......Page 476
Throat impedance......Page 480
Theoretical considerations......Page 481
Resultant field......Page 563
Axisymmetric solutions to the shell wave equations......Page 483
Throat impedance......Page 484
Flare constant and throat impedance......Page 485
Cutoff frequency......Page 486
Theoretical considerations......Page 487
Eigenvalues with zero load at the perimeter......Page 757
Transmission parameters......Page 489
Reverse horn......Page 490
Finite conical horn......Page 491
Solution of the free-space wave equation......Page 492
Truncation effects......Page 493
Nonlinear distortion......Page 495
9.15 Cross-sectional shapes......Page 500
9.16 Materials......Page 501
References......Page 511
Part XXXVIII: Membranes......Page 513
10.3 Normal modes and normal frequencies......Page 514
Sound pressure at normal modes......Page 522
Loudness......Page 523
Resonance curve......Page 528
Definitions......Page 838
10.6 Basic matters......Page 535
13.7 Radiation from a rigid circular piston in an infinite baffle......Page 537
10.9 Total steady sound pressure level......Page 538
Definitions......Page 840
Reverberant steady-state sound pressure......Page 539
10.10 Optimum reverberation time......Page 540
10.12 Early and reverberant sound in concert halls......Page 541
10.13 Distance for equality of direct and reverberant sound fields......Page 542
10.14 Sound levels for speech and music......Page 544
References......Page 546
Further Reading......Page 547
Direct sound......Page 548
Strength and quality of the reverberant sound field......Page 549
Reverberation times......Page 550
Calculation of the velocity series coefficients......Page 551
References......Page 553
12.2 Radiation from an infinite line source......Page 555
12.3 Scattering of a plane wave from a rigid sphere......Page 556
Far-field pressure......Page 560
Radiation impedance......Page 562
Near-field pressure......Page 568
Near-field pressure......Page 573
Radiation impedance......Page 576
12.7 Radiation from a rectangular cap in a sphere......Page 578
Near-field pressure......Page 580
Far-field pressure......Page 582
12.8 Radiation from a piston in a sphere......Page 583
Near-field pressure......Page 584
Radiation impedance......Page 588
12.9 Radiation from an oscillating convex dome in an infinite baffle......Page 589
Near-field pressure......Page 590
Far-field pressure......Page 593
Near-field pressure......Page 597
Far-field pressure......Page 600
Radiation impedance......Page 601
References......Page 604
13.3 The Kirchhoff–Helmholtz boundary integral......Page 609
Rectangular coordinates—near-field......Page 612
Proof of the Fourier Green's function in rectangular coordinates......Page 613
Cylindrical coordinates......Page 615
Spherical coordinates......Page 617
Spherical–cylindrical coordinates—near-field......Page 619
13.5 Boundary integral method case study: radially pulsating cap in a rigid sphere......Page 620
13.6 Reflection of a point source from a plane......Page 623
Part XXXVI: Radiation and scattering in cylindrical-spherical coordinates......Page 625
Integrals......Page 841
Far-field pressure......Page 628
Near-field pressure......Page 630
Radiation impedance and high-frequency asymptotic expression......Page 634
Boundary conditions......Page 636
Near-field pressure......Page 639
Surface velocity......Page 640
Radiation admittance and low-frequency asymptotic surface velocity......Page 643
Relationship between a resilient disk in free space and a rigid piston in an infinite baffle......Page 646
Boundary conditions......Page 647
Surface velocity......Page 655
Radiation admittance......Page 656
Boundary conditions......Page 659
Formulation of the coupled equation......Page 661
Solution of the power series coefficients for a piston in a circular baffle......Page 663
Far-field pressure......Page 665
Near-field pressure......Page 668
Radiation impedance of a piston in a circular baffle......Page 673
Far-field pressure......Page 677
Radiation impedance......Page 679
Bouwkamp theory......Page 683
Reflection from plane rigid objects [31]......Page 684
Reflection from plane resilient objects......Page 686
The Babinet–Bouwkamp principle for diffraction through a circular aperture in a rigid screen......Page 687
The Babinet–Bouwkamp principle for diffraction through a circular aperture in a resilient screen......Page 688
Part XXXVII: Radiation theorems, radiation in rectangular-spherical coordinates, mutual impedance......Page 690
Boundary conditions......Page 691
Far-field pressure......Page 692
Radiation impedance......Page 694
Two-dimensional system......Page 695
Three-dimensional system......Page 697
Axisymmetric three-dimensional system......Page 698
13.16 The bridge product theorem......Page 699
Far-field pressure......Page 701
Radiation impedance......Page 702
Boundary conditions......Page 703
Directivity......Page 705
Impedance......Page 707
Array of pistons......Page 711
The forward problem......Page 713
13.20 Time reversal......Page 715
References......Page 717
14.2 Membrane wave equation in rectangular coordinates......Page 720
14.3 Solution of the membrane wave equation for a rectangular membrane......Page 722
14.7 Solution of the membrane wave equation for a circular membrane......Page 726
14.9 Green's function for a circular membrane......Page 727
Boundary conditions......Page 730
Solution of the membrane wave equation......Page 733
Solution of the free-space wave equation......Page 734
Final set of simultaneous equations for the power-series coefficients......Page 735
14.11 Plate wave equation in polar coordinates......Page 739
14.12 Solution of the plate wave equation for a circular plate......Page 740
14.13 Modes of a clamped circular plate......Page 741
14.14 Modes of a simply supported circular plate......Page 742
14.15 Modes of a free circular plate......Page 745
14.16 Shell wave equation in polar coordinates......Page 746
14.17 Green's function for a shallow spherical shell......Page 748
Boundary conditions......Page 751
Coil impedance at the perimeter......Page 755
Calculation of the eigenvalues......Page 756
Eigenvalues with infinite load at the perimeter......Page 758
Eigenfunctions......Page 759
Solution of the wave equation for the shell in an infinite baffle......Page 760
Velocity distribution......Page 761
Far-field pressure......Page 764
14.19 Radiation from a circular plate in an infinite baffle—model of an induction loudspeaker coupled to its surrounding air [13,14]......Page 768
Construction of an induction loudspeaker......Page 769
Analogous circuit......Page 771
Boundary conditions......Page 775
Far-field pressure of a free plate with an evenly distributed radiation load......Page 779
References......Page 788
15.2 Construction......Page 790
15.3 Directivity control......Page 792
15.4 Continuous delay......Page 793
Part XXXXIV: Lumped-element model of an electrostatic loudspeaker......Page 812
15.12 Static membrane compliance......Page 814
15.14 Setting tension to limit displacement and maintain stability......Page 816
15.15 Radiation impedance......Page 817
15.16 Frequency response......Page 818
15.17 Summary of electrostatic loudspeaker design......Page 824
References......Page 830
Gamma function......Page 835
Bessel......Page 831
Odd order......Page 832
Chebyshev......Page 833
Hyperbolic formulas......Page 836
Derivatives......Page 839
Integral representations......Page 842
Limiting forms for small arguments......Page 843
Asymptotic forms for very large arguments......Page 844
Integrals......Page 845
Definitions......Page 848
Limiting forms for small arguments......Page 849
Recursion formulas......Page 850
Definitions......Page 851
Asymptotic forms for large arguments......Page 852
Dirac delta function......Page 853
APPENDIX
III - Answers to problems......Page 855
B......Page 868
C......Page 869
D......Page 870
E......Page 871
G......Page 872
I......Page 873
M......Page 874
P......Page 875
R......Page 876
S......Page 877
Z......Page 878
Back Cover......Page 879
