Room Acoustics

323 Pages·2016·6.8 MB·English

by  Heinrich Kuttruff

S i x t h E d i t i o n
Room
Acoustics

S i x t h E d i t i o n
Room
Acoustics
Heinrich Kuttruff
Institute of Technical Acoustics
Aachen University, Germany
Boca Raton London New York
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Version Date: 20160801
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Library of Congress Cataloging-in-Publication Data
Names: Kuttruff, Heinrich, author.
Title: Room acoustics / Heinrich Kuttruff.
Description: Sixth edition. | Boca Raton : CRC Press, [2017] | Includes
bibliographical references and index.
Identifiers: LCCN 2016034244 | ISBN 9781482260434
Subjects: LCSH: Architectural acoustics.
Classification: LCC NA2800 .K87 2017 | DDC 729/.29--dc23
LC record available at https://lccn.loc.gov/2016034244
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Contents
List of symbols ix
Preface xiii
Acknowledgments xv
Introduction xvii
1 Some facts on sound waves, sources and hearing 1
1.1 Basic relations – The wave equation 1
1.2 Plane waves and spherical waves 3
1.3 Energy density and intensity, radiation 7
1.4 Signals and systems 9
1.5 Sound pressure level and sound power level 14
1.6 Some properties of human hearing 15
1.7 Sound sources 18
References 22
2 Reflection and scattering 23
2.1 Reflection factor, absorption coefficient and wall impedance 23
2.2 Reflection of plane waves 25
2.3 A few examples 30
2.4 Reflection of spherical waves 36
2.5 Random sound incidence 38
2.6 Reflection from finite-sized plane surfaces 42
2.7 Scattering by boundary irregularities 45
References 50
3 Sound waves in a room 51
3.1 Formal solution of the wave equation 52
3.2 Normal modes in a rectangular room with rigid boundaries 54
3.3 Number and density of eigenfrequencies 58
3.4 Non-rigid walls 60
3.5 Numerical solution of the wave equation: The finite element method 63
3.6 Steady-state sound field 66
v
vi Contents
3.7 Some properties of room transfer functions 70
3.8 Decaying modes, reverberation 75
References 78
4 Geometrical room acoustics 81
4.1 Enclosures with plane walls, image sources 81
4.2 The temporal distribution of reflections 86
4.3 The directional distribution of reflections, diffuse sound field 90
4.4 Enclosures with curved walls 92
4.5 Radiosity integral 95
4.6 Modifications and generalizations, diffusion equation 99
References 102
5 Reverberation and steady-state energy density 103
5.1 Diffuse sound fields, elementary theory of sound decay 104
5.2 Factors influencing sound field diffuseness 106
5.3 Mean free path length and average rate of reflections 108
5.4 Non-uniform boundary absorption 111
5.5 The influence of unequal path lengths 114
5.6 Enclosure driven by a sound source 116
5.7 Applications of the radiosity integral: The influence
of imperfect diffuseness 120
References 124
6 Sound absorption and sound absorbers 125
6.1 Energy losses in the medium 125
6.2 Sound absorption by membranes and perforated sheets 128
6.3 Resonance absorbers 131
6.4 Helmholtz resonators 134
6.5 Sound propagation in porous materials, the Rayleigh model 137
6.6 Porous absorbers 141
6.7 Audience and seat absorption 146
6.8 Anechoic rooms 151
References 154
7 Subjective room acoustics 157
7.1 Sound pressure level, strength factor 158
7.2 Some general remarks on reflections and echoes 159
7.3 The perception of reflections and echoes 160
7.4 Echoes and colouration 163
7.5 Parameters characterizing the “early energy” 168
7.5.1 Definition 168
7.5.2 Clarity index 169
7.5.3 Centre time 170
Contents vii
7.5.4 Speech transmission index 171
7.5.5 Support 173
7.6 Reverberation and reverberance 174
7.7 Spaciousness of sound fields 180
7.8 Assessment of concert hall acoustics 182
References 190
8 Measuring techniques in room acoustics 193
8.1 General remarks on instrumentation 193
8.2 Measurement of the impulse response 196
8.3 Examination of the impulse response 201
8.4 Measurement of reverberation 207
8.5 Directional distribution, diffuseness of a sound field 211
8.6 Sound absorption – Tube methods 218
8.7 Sound absorption – Reverberation chamber 221
8.8 Scattering coefficient 225
References 228
9 Design considerations and design procedures 231
9.1 Prediction of noise level 232
9.2 Direct sound 236
9.3 Examination of room shape 238
9.4 Reverberation time 243
9.5 More on concert halls 247
9.6 Multipurpose halls 250
9.7 Acoustical scale models 252
9.8 Computer simulation 254
9.9 Auralization, virtual reality 260
References 265
10 Electroacoustical systems in rooms 267
10.1 Loudspeakers 268
10.2 Required power and reach of a loudspeaker 272
10.3 Remarks on loudspeaker positions 275
10.4 Acoustical feedback and its suppression 278
10.5 Reverberation enhancement with external reverberators 283
10.6 Reverberation enhancement by controlled feedback 289
References 293
Index 295

List of symbols
LATIN CAPITAL LETTERS
A constant, equivalent absorption area, absorption cross-section
B constant, frequency bandwidth, irradiation density
C constant, clarity index, circumference
C correlation matrix
D diameter, thickness, definition, diffusion constant
D diagonal matrix (in Section 7.8)
E energy
F force, arbitrary function
G strength factor
G(ω), G(f) transfer function, arbitrary function
H transfer function, distribution of damping constants
IACC interaural cross correlation
J (z) Bessel function of order n
n
K normalization constant
n
K(r,r′) kernel (of integral equation)
K stiffness matrix (in Section 3.5)
L length, sound pressure level
LEF lateral energy fraction
M mass
M mass matrix (in Section 3.5)
M′ specific mass (= mass per unit area)
N integer
P power, probability
PL sound power level
Q volume velocity, quality factor
Q scattering cross-section
s
R reflection factor, distance, radius of curvature, resistance
R radiation resistance
r
S area
S(ω), S(f) spectral density or spectral function
SPL sound pressure level
T period of an oscillation, transmission factor, reverberation or decay time
V volume
W(ω), W(f) power spectrum
W(r,r′) propagator (in Section 10.5)
W transformation matrix (in Section 7.8)
ix