Preface ...................................................... xiii
Acknowledgements ............................................... xv
CHAPTER 1 Introduction and terminology ......................... 1
Part I: Introduction ............................................ 1
1.1 A little history ........................................... 1
1.2 What is sound? ............................................. 5
1.3 Propagation of sound through gas ........................... 7
1.4 Measurable aspects of sound ................................ 9
Part II: Terminology ........................................... 10
1.5 General ................................................... 10
1.6 Standard International (SI) units ......................... 12
1.7 Pressure and density ...................................... 12
1.8 Speed and velocity ........................................ 13
1.9 Impedance ................................................. 14
1.10 Intensity, energy density, and levels ..................... 14
CHAPTER 2 The wave equation and solutions ..................... 21
Part III: The wave equation .................................... 21
2.1 Introduction .............................................. 21
2.2 Derivation of the wave equation ........................... 22
Part IV: Solutions of the wave equation in one dimension ....... 29
2.3 General solutions of the one-dimensional wave equation .... 29
2.4 Solution of wave equation for air in a tube terminated
by an impedance ........................................... 37
2.5 Solution of wave equation for air in a tube filled with
absorbent material ........................................ 46
2.6 Freely traveling plane wave ............................... 47
2.7 Freely traveling cylindrical wave ......................... 48
2.8 Freely traveling spherical wave ........................... 51
Part V: Solutions of the Helmholtz wave equation in three
dimensions ..................................................... 54
2.9 Rectangular coordinates ................................... 54
2.10 Cylindrical coordinates ................................... 55
2.11 Spherical coordinates ..................................... 59
CHAPTER 3 Electro-mechano-acoustical circuits ................. 65
Part VI: Mechanical circuits ................................... 65
3.1 Introduction .............................................. 65
3.2 Physical and mathematical meanings of circuit elements .... 66
3.3 Mechanical elements ....................................... 69
Part VII: Acoustical circuits .................................. 84
3.4 Acoustical elements ....................................... 84
3.4 Part VIII: Transducers .................................... 94
3.5 Electromechanical transducers ............................. 94
3.6 Mechano-acoustic transducer .............................. 101
3.7 Examples of transducer calculations ...................... 102
Part IX: Circuit theorems, energy, and power .................. 104
3.8 Conversion from admittance-type analogies to
impedance-type analogies ................................. 104
3.9 Thevenin's theorem ....................................... 106
3.10 Transducer impedances .................................... 107
CHAPTER 4 Acoustic components ................................ 119
4.1 Introduction ............................................. 119
Part X: Acoustic elements ..................................... 120
4.2 Acoustic mass (inertance) ................................ 120
4.3 Acoustic compliances ..................................... 121
4.4 Acoustic resistances ..................................... 125
4.5 Cavity with holes on opposite sides—mixed
mass-compliance element .................................. 128
4.6 Intermediate-sized tube-mixed mass-resistance element .... 129
4.7 Perforated sheet—mixed mass-resistance element ........... 130
4.8 Acoustic transformers .................................... 131
Part XI: Elementary reflection and radiation of sound ......... 136
4.9 Reflection of a plane wave from a plane .................. 137
4.10 Radiation from a pulsating sphere ........................ 139
4.11 Radiation from a monopole point source (simple source) ... 142
4.12 Combination of point sources in phase .................... 143
4.13 Steered beam-forming array of point sources .............. 148
4.14 Dipole point source (doublet) ............................ 153
4.15 Radiation from an oscillating sphere ..................... 157
Part XII: Directivity index ................................... 162
4.16 Directivity index and directivity factor ................. 162
Part ХIII: Radiation impedances ............................... 167
4.17 Pulsating sphere ......................................... 167
4.18 Oscillating sphere ....................................... 169
4.19 Plane circular piston in infinite baffle ................. 170
4.20 Plane circular free disk ................................. 175
4.21 Plane circular piston radiating from one side only in
free space ............................................... 176
Part XIV: Viscous and thermal losses .......................... 178
4.22 Sound in lossy tubes ..................................... 178
4.23 Wave equation for an infinite lossy tube ................. 180
CHAPTER 5 Microphones ........................................ 199
Part XV: General characteristics of microphones ............... 199
5.1 Pressure microphones ..................................... 200
5.2 Pressure-gradient microphones ............................ 202
5.3 Combination pressure and pressure-gradient microphones ... 206
Part XVI: Pressure microphones ................................ 208
5.4 Electromagnetic moving-coil microphone (dynamic
microphone) .............................................. 208
5.5 Electrostatic microphone (capacitor microphone) .......... 216
Part XVII: Pressure-gradient microphones ...................... 225
5.6 Electromagnetic Ribbon microphones ....................... 225
Part XVIII: Combination microphones ........................... 228
5.7 Electrical combination of pressure and pressure-
gradient transducers ..................................... 228
5.8 Acoustical combination of pressure and
pressure-gradient microphones ............................ 230
5.9 Dual-diaphragm combination of pressure and
pressure-gradient microphones ............................ 231
CHAPTER 6 Electrodynamic loudspeakers ........................ 241
Part XIX: Basic theory of electrodynamic loudspeakers ......... 241
6.1 Introduction ............................................. 241
6.2 Construction ............................................. 242
6.3 Electro-mechano-acoustical circuit ....................... 244
6.4 Power output ............................................. 251
6.5 Thiele-Small parameters .................................. 252
6.6 Sound pressure produced at distance r .................... 253
6.7 Frequency-response curves ................................ 255
6.8 Electrical input impedance ............................... 256
6.9 Efficiency ............................................... 257
6.10 Measurement of Thiele-Small parameters ................... 259
6.11 Examples of loudspeaker calculations ..................... 262
Part XX: Design factors affecting direct-radiator
loudspeaker performance ....................................... 263
6.12 Magnet size .............................................. 264
6.13 Voice-coil design ........................................ 267
6.14 Diaphragm behavior ....................................... 270
6.15 Directivity characteristics .............................. 273
6.16 Transfer functions and the Laplace transform ............. 275
6.17 Transient response ....................................... 277
6.18 Nonlinearity ............................................. 282
CHAPTER 7 Loudspeaker systems ................................ 289
Part XXI: Simple enclosures ................................... 290
7.1 Brief summary of common loudspeaker systems .............. 291
7.2 Unbaffled direct-radiator loudspeaker .................... 292
7.3 Infinite baffle .......................................... 294
7.4 Finite-sized flat baffle ................................. 294
7.5 Open-back cabinets ....................................... 295
7.6 Closed-box baffle ........................................ 295
7.7 Measurement of baffle constants .......................... 320
Part ХХII: Bass-reflex enclosures ............................. 329
7.8 General description ...................................... 329
7.9 Acoustical circuit ....................................... 329
7.10 Electro-mechano-acoustical circuit ....................... 331
7.11 Radiated sound ........................................... 334
7.12 Alignments for predetermined frequency-response shapes ... 335
7.13 Port dimensions .......................................... 339
7.14 Diaphragm displacement ................................... 340
7.15 Electrical input impedance and evaluation of Ql .......... 340
7.16 Performance .............................................. 342
7.17 Construction and adjustment notes ........................ 343
Part XXIII: 2-port network for small enclosures ............... 352
7.18 2-port network for a bass-reflex enclosure ............... 352
Part XXIV: Transmission-line enclosures ....................... 358
7.19 Transmission-Line Enclosures ............................. 358
Part XXV: Multiple Drive Units ................................ 373
7.20 Crossover filters ........................................ 373
7.21 Dual concentric drive units .............................. 388
CHAPTER 8 Cellphone acoustics ................................ 391
Part XXVI: Acoustical transducers for cellphones .............. 391
8.1 Loudspeaker and microphone ............................... 391
8.2 Circuit diagram for a cellphone loudspeaker .............. 393
8.3 Design considerations .................................... 395
8.4 Head and torso simulator ................................. 396
8.5 Microphones .............................................. 397
Part XXVII: Type approval testing of cellphones ............... 402
8.6 Measurements for type approval ........................... 402
CHAPTER 9 Horn loudspeakers .................................. 407
Part XXVIII: Horn drive units ................................. 407
9.1 Introduction ............................................. 407
9.2 Electro-mechano-acoustical circuit ....................... 408
9.3 Reference efficiency ..................................... 410
9.4 Frequency response ....................................... 412
9.5 Examples of horn calculations ............................ 416
Part XXK: Horns ............................................... 417
9.6 General description ...................................... 417
9.7 Possible profiles ........................................ 417
9.8 Mouth size ............................................... 419
9.9 Infinite parabolic horn .................................. 419
9.10 Infinite conical horn .................................... 421
9.11 Infinite exponential horn ................................ 422
9.12 Infinite hyperbolic horn (hypex) ......................... 425
9.13 Finite horns ............................................. 428
9.14 Bends in horns ........................................... 435
9.15 Cross-sectional shapes ................................... 438
9.16 Materials ................................................ 438
CHAPTER 10 Sound in enclosures ................................ 449
Part XXX: Sound fields in small, regularly shaped enclosures .. 449
10.1 Introduction ............................................. 449
10.2 Stationary and standing waves ............................ 450
10.3 Normal modes and normal frequencies ...................... 450
10.4 Steady-state and transient sound pressures ............... 458
10.5 Examples of rectangular enclosures ....................... 467
Part XXXI: Sound in large enclosures .......................... 469
10.6 Basic matters ............................................ 469
10.7 The reverberation equations .............................. 470
10.8 Air absorption ........................................... 472
10.9 Total steady sound-pressure level ........................ 472
10.10 Optimum reverberation time .............................. 473
10.11 Sound Strength G ........................................ 473
10.12 Early and reverberant sound in concert halls ............ 475
10.13 Distance for equality of direct and reverberant sound
fields .................................................. 476
10.14 Sound levels for speech and music ....................... 477
CHAPTER 11 Room design for loudspeaker listening .............. 481
Part XXXII: Home room design .................................. 481
11.1 Concert hall acoustics ................................... 481
11.2 Listening room acoustics ................................. 483
CHAPTER 12 Radiation and scattering of sound by the boundary
value method .................................................. 487
Part ХХХIII: Radiation in cylindrical coordinates ............. 487
12.1 Radiation from a pulsating infinite cylinder ............. 487
12.2 Radiation from an infinite line source ................... 488
Part XXXIV: Radiation and scattering in spherical
coordinates ................................................... 489
12.3 Scattering of a plane wave from a rigid sphere ........... 489
12.4 Scattering from a rigid sphere by a point source ......... 494
12.5 Radiation from a point source on a sphere ................ 499
12.6 Radiation from a spherical cap in a sphere ............... 503
12.7 Radiation from a rectangular cap in a sphere ............. 509
12.8 Radiation from a piston in a sphere ...................... 515
12.9 Radiation from an oscillating convex dome in an
infinite baffle .......................................... 520
12.10 Radiation from an oscillating concave dome in an
infinite baffle .......................................... 526
CHAPTER 13 Radiation and scattering of sound by the
boundary integral method ...................................... 535
Part XXXV: Boundary integrals and the Green's function ........ 536
13.1 The Huygens-Fresnel principle ............................ 536
13.2 The Rayleigh integrals and Green's function .............. 536
13.3 The Kirchhoff-Helmholtz boundary integral ................ 539
13.4 The Green's function in different coordinate systems ..... 541
13.5 Boundary integral method case study: Radially pulsating
cap in a rigid sphere .................................... 548
13.6 Reflection of a point source from a plane ................ 551
Part XXXVI: Radiation and scattering in cylindrical-
spherical coordinates ......................................... 553
13.7 Radiation from a rigid circular piston in an infinite
baffle ................................................... 553
13.8 Radiation from a resilient circular disk without
a baffle ................................................. 562
13.9 Radiation from a resilient disk in an infinite baffle .... 572
13.10 Radiation from a rigid circular piston in a finite
circular open baffle .................................... 582
13.11 Radiation from a rigid circular piston in a finite
circular closed baffle (one-sided radiator) ............. 597
1 13.12 The Babinet-Bouwkamp principle ........................ 602
Part XXXVII: Radiation theorems, radiation in rectangular-
spherical coordinates, mutual impedance ....................... 609
13.13 The Bouwkamp impedance theorem .......................... 609
13.14 Radiation from an infinitely long oscillating strip in
an infinite baffle ...................................... 610
13.15 The far-field pressure distribution as a spatial
frequency spectrum of the source velocity distribution .. 614
13.16 The bridge product theorem .............................. 618
13.17 Radiation from a rigid rectangular piston in an
infinite baffle ......................................... 618
13.18 Mutual radiation impedance between rigid circular
pistons in an infinite baffle ........................... 621
13.19 Near-field acoustical holography ........................ 627
13.20 Time-reversal ........................................... 629
CHAPTER 14 State variable analysis of circuits ................ 633
14.1 A brief history .......................................... 633
14.2 What is state variable analysis? ......................... 634
14.3 Why use state variable analysis? ......................... 634
14.4 What are the restrictions? ............................... 635
14.5 Some basic circuit theory ................................ 635
14.6 Graph theory ............................................. 636
14.7 Worked example No. 1: Loudspeaker in an enclosure with
a bass-reflex port ....................................... 638
14.8 Solution of the worked example using the Faddeev-
Leverrier algorithm ...................................... 648
14.9 Far-field on-axis pressure ............................... 650
14.10 Worked example No. 2: Loudspeaker in an enclosure with
a bass-reflex port using the Norton equivalent source ... 652
14.11 Worked example No. 3: Loudspeaker in an enclosure with
a bass-reflex port using a transformer and gyrator ...... 655
14.12 Worked example No. 4: Loudspeaker in an enclosure
with a bass-reflex port using controlled sources ........ 662
14.13 Gyrator comprising two current-controlled voltage
sources ................................................. 669
APPENDIX I Frequency-response shapes for Loudspeakers ......... 671
APPENDIX II Mathematical formulas ............................. 675
APPENDIX III Conversion factors ............................... 691
Index ......................................................... 697
DESIGN SUMMARIES
Summary of closed-box baffle design ........................... 296
Summary of bass-reflex design ................................. 332
Summary of transmission-line design ........................... 359
SELECTED TABLES
1.1 List of SI units .......................................... 12
2.1 Termination impedances, standing wave ratios, and
reflection coefficients for three types of tube
termination ............................................... 39
2.2 General and steady-state relations for small-signal
sound propagation in gases ................................ 54
3.1 Mathematical and physical significance of symbols ......... 67
3.2 Values of elements in electrical, mechanical, and
acoustical circuits ....................................... 68
3.3 Conversion from admittance-type analogy to impedance-
type analogy, or vice versa ............................... 70
4.1 Specific acoustic resistances of dust screens ............ 126
4.3 Calculation of directivity index DI(ƒ) ................... 167
4.4 Radiation impedance and admittance for one side of a
plane circular piston in an infinite baffle .............. 174
4.5 Radiation impedance and admittance for one side of a
plane circular piston in free space ...................... 176
4.6 Radiation impedance and admittance for a plane circular
piston radiating from one side only in free space ........ 179
5.2 Dual-diaphragm condenser microphone parameters ........... 239
6.1 Resistivity and density of various metals ................ 268
6.3 Overview of nonlinearities in electrodynamic
loudspeakers ............................................. 282
7.1 Coefficients which give the characteristic impedance
and wave number of a homogenous absorbent material ....... 306
10.1 Air attenuation constant m as a function of frequency,
temperature, and relative humidity ....................... 472
10.2 Maximum peak sound pressure levels due to various sound
sources .................................................. 478
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