Preface to the first edition ................................ ix
Preface to the second edition ............................. xiii
Acknowledgements ........................................... xiv
Glossary of frequently used symbols ......................... xv
Introduction .................................................... 1
Absorption versus diffuse reflections ........................ 4
1 Applications and basic principles of absorbers ............... 7
1.1 Reverberation control ................................... 7
1.2 Noise control in factories and large rooms with
diffuse fields ......................................... 13
1.3 Modal control in critical listening spaces ............. 14
1.4 Echo control in auditoria and lecture theatres -
basic sound propagation models ......................... 16
1.5 Absorption in sound insulation - transfer matrix
modelling .............................................. 22
1.6 Pipes, ducts and silencers - porous absorber
characteristics ........................................ 24
1.7 Enclosures, barriers and roads ......................... 26
1.8 Natural noise control .................................. 28
1.9 Hearing protection devices ............................. 28
1.10 Loudspeaker cabinets ................................... 28
1.11 Summary ................................................ 29
1.12 References ............................................. 29
2 Applications and basic principles of diffusers .............. 31
2.1 Echo control in auditoria .............................. 31
2.2 Reducing coloration in small sound reproduction
rooms .................................................. 40
2.3 Music practice rooms ................................... 49
2.4 Promoting diffuse fields in reverberation chambers ..... 52
2.5 Improving speech intelligibility in underground or
subway stations ........................................ 53
2.6 Promoting spaciousness in auditoria .................... 54
2.7 Reducing effects of early arriving reflections in
large spaces ........................................... 55
2.8 Stage enclosures ....................................... 56
2.9 Blurring the focussing from concave surfaces ........... 63
2.10 In audience areas - diffuse fields ..................... 64
2.11 Barriers and streets ................................... 66
2.12 Conclusions ............................................ 67
2.13 References ............................................. 67
3 Measurement of absorber properties .......................... 70
3.1 Impedance or standing wave tube measurement ............ 70
3.2 Two-microphone free field measurement .................. 80
3.3 Multi-microphone techniques for non-isotropic,
non-planar surfaces .................................... 82
3.4 Reverberation chamber method ........................... 84
3.5 In situ measurement of absorptive properties ........... 90
3.6 Measurement of internal properties of porous
absorbents ............................................. 95
3.7 Summary ............................................... 107
3.8 References ............................................ 107
4 Measurement and characterization of diffuse reflections
or scattering .............................................. 110
4.1 Measurement of scattered polar responses .............. 111
4.2 Diffusion and scattering coefficients - a general
discussion ............................................ 127
4.3 The need for coefficients ............................. 128
4.4 The diffusion coefficient ............................. 130
4.5 The scattering coefficient ............................ 135
4.6 The correlation scattering coefficient - from polar
responses to scattering coefficients .................. 143
4.7 Contrasting diffusion and scattering coefficients -
a summary ............................................. 147
4.8 Other methods for characterizing diffuse
reflections ........................................... 147
4.9 Summary ............................................... 153
4.10 References ............................................ 153
5 Porous absorption .......................................... 156
5.1 Absorption mechanisms and characteristics ............. 156
5.2 Some material types ................................... 160
5.3 Basic material properties ............................. 169
5.4 Modelling propagation within porous absorbents ........ 172
5.5 Predicting the surface impedance and absorption
coefficient of porous absorbers ....................... 184
5.6 Local and extended reaction ........................... 189
5.7 Oblique incidence ..................................... 189
5.8 Biot theory for elastic framed material ............... 191
5.9 Summary ............................................... 192
5.10 References ............................................ 193
6 Resonant absorbers ......................................... 196
6.1 Mechanisms ............................................ 197
6.2 Example constructions ................................. 198
6.3 Design equations: resonant frequency .................. 208
6.4 Example calculations .................................. 221
6.5 Other constructions ................................... 223
6.6 Summary ............................................... 228
6.7 References ............................................ 228
7 Some other absorbers ....................................... 230
7.1 Seating and audience .................................. 230
7.2 Absorbers from Schroeder diffusers .................... 232
7.3 Absorbing sonic crystals .............................. 244
7.4 Trees and vegetation .................................. 248
7.5 Summary ............................................... 249
7.6 References ............................................ 250
8 Prediction of scattering ................................... 252
8.1 Boundary element methods .............................. 252
8.2 Kirchhoff ............................................. 268
8.3 Fresnel ............................................... 272
8.4 Fraunhofer or Fourier solution ........................ 273
8.5 Finite difference time domain (FDTD) .................. 277
8.6 Other methods ......................................... 284
8.7 Summary ............................................... 286
8.8 References ............................................ 287
9 Schroeder diffusers ........................................ 289
9.1 Basic principles ...................................... 289
9.2 Design equations ...................................... 291
9.3 Some limitations and other considerations ............. 292
9.4 Sequences ............................................. 295
9.5 The curse of periodicity and modulation ............... 303
9.6 Improving the bass response ........................... 312
9.7 Multi-dimensional devices ............................. 315
9.8 Absorption ............................................ 319
9.9 But ................................................... 322
9.10 Optimization .......................................... 324
9.11 Summary ............................................... 329
9.12 References ............................................ 329
10 Geometric reflectors and diffusers ......................... 331
10.1 Plane surfaces ........................................ 331
10.2 Triangles and pyramids ................................ 339
10.3 Concave arcs .......................................... 343
10.4 Convex arcs ........................................... 344
10.5 Optimized curved surfaces ............................. 352
10.6 Fractals .............................................. 364
10.7 Volumetric diffusers .................................. 368
10.8 Materials ............................................. 369
10.9 Summary ............................................... 371
10.10 References ........................................... 371
11 Hybrid surfaces ............................................ 373
11.1 Planar hybrid surface ................................. 373
11.2 Curved hybrid surfaces ................................ 375
11.3 Ternary and quadriphase surfaces ...................... 377
11.4 Simplest theory ....................................... 377
11.5 Number sequences ...................................... 378
11.6 Absorption ............................................ 389
11.7 Accuracy of the Fourier theory ........................ 390
11.8 Diffuse reflections ................................... 393
11.9 Summary ............................................... 398
11.10 References ........................................... 398
12 Absorbers and diffusers in rooms and geometric models ..... 399
12.1 Converting absorption coefficients .................... 399
12.2 Absorption in geometric room acoustic models .......... 404
12.3 Diffuse reflections in geometric room acoustic
models ................................................ 407
12.4 Summary ............................................... 417
12.5 References ............................................ 417
13 Active absorbers and diffusers ............................. 419
13.1 Some principles of active control ..................... 420
13.2 An example active impedance system and a general
overview .............................................. 422
13.3 Active absorption in ducts ............................ 425
13.4 Active absorption in three dimensions ................. 425
13.5 Hybrid active-passive absorption ...................... 431
13.6 Active diffusers ...................................... 434
13.7 Summary ............................................... 438
13.8 References ............................................ 438
Appendix A
A.l Table of absorption coefficients ....................... 440
A.2 References ............................................. 444
Appendix В
MATLAB scripts ............................................. 446
Appendix С
C.l Normalized diffusion coefficient table ................. 453
C.2 Correlation scattering coefficient table ............... 458
Index ...................................................... 463
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