Sound Insulation in Buildings

477 Pages·2017·15.146 MB·\477

by  Jens Holger Rindel (Author)

Sound Insulation in
Buildings

Sound Insulation in
Buildings
Jens Holger Rindel
Cover photo by Iiris Turunen-Rindel. The photo on the cover shows a concrete building from the
1960s being demolished.
CRC Press
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Library of Congress Cataloging-in-Publication Data
Names: Rindel, J. H. (Jens Holger), author.
Title: Sound insulation in buildings / by Jens Holger Rindel.
Description: Boca Raton : CRC Press, [2018] | Includes bibliographical
references and index.
Identifiers: LCCN 2017024121| ISBN 9781498700412 (hardback : alk. paper) |
ISBN 9781498700429 (ebook : alk. paper)
Subjects: LCSH: Soundproofing. | Architectural acoustics.
Classification: LCC TH1725 .R56 2018 | DDC 693.8/34--dc23
LC record available at https://lccn.loc.gov/2017024121
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Contents
Preface xv
About the Author xix
Introduction xxi
1 Basic concepts in acoustics 1
1.1 Introduction 1
1.2 The decibel scale 2
1.3 Frequency and related concepts 3
1.3.1 Harmonic vibrations 3
1.3.2 Speed of sound 4
1.3.3 Frequency bands 4
1.4 Loudness level and A-weighted sound pressure level 6
1.5 Propagation of sound in plates 8
1.5.1 Longitudinal waves 9
1.5.2 Bending and shear waves in plates 9
1.5.3 Critical frequency 12
1.6 Averaging 14
1.6.1 Arithmetic average 14
1.6.2 Geometric average 14
1.6.3 Harmonic average 14
1.6.4 Energetic average 14
1.7 Useful mathematical functions and formulae 15
1.7.1 Trigonometrical formulae 15
1.7.2 Euler’s formulae 15
1.7.3 The cardinal sine function 15
1.7.4 Logarithmic functions 15
1.7.5 Basic equations for complex numbers 16
References 17
vi Contents
2 Mechanical vibrations 19
2.1 A simple mechanical system 19
2.2 Mechanical impedance and mobility 21
2.3 Free vibrations 23
2.4 Forced vibrations 26
2.5 Resonance 30
2.5.1 Resonance frequency 30
2.5.2 Bandwidth of a resonant system 31
2.6 Vibration insulation 33
2.6.1 The power input 33
2.6.2 Force transmitted to the foundation 34
2.6.3 Vibration isolators with hysteretic damping 37
2.6.4 The Q-factor 37
2.6.5 Insertion loss 38
2.6.6 Insulation against structure-borne vibrations 40
2.6.7 Design of vibration isolators 42
2.7 Human response to vibrations 44
2.7.1 Examples of evaluation criteria 46
References 47
3 The sound field in front of a wall 49
3.1 Normal incidence of a plane wave 49
3.2 Oblique incidence of a plane wave 52
3.3 Random incidence in a diffuse sound field 54
3.4 The sound field at edges and corners in a room 59
3.5 The influence of bandwidth on reflection of noise 61
References 67
4 Introduction to room acoustics 69
4.1 Sound waves in rooms 69
4.1.1 Standing waves in a rectangular room 69
4.1.2 Modal reverberation times 72
4.1.3 Transfer function in a room 74
4.1.4 Modal density 74
4.1.5 The Schroeder limiting frequency 79
4.2 Statistical room acoustics 79
4.2.1 The diffuse sound field 79
4.2.2 Incident sound power on a surface 80
4.2.3 Equivalent absorption area 82
4.2.4 Energy balance in a room 82
Contents vii
4.2.5 Reverberation time: Sabine’s formula 83
4.2.6 Stationary sound field in a room:
Reverberation distance 85
4.3 Geometrical room acoustics 89
4.3.1 Sound rays and a general reverberation formula 89
4.3.2 Sound absorption in air 91
4.3.3 Reflection density in a room 92
4.4 Calculation of reverberation time 93
4.4.1 Using Sabine’s formula 93
4.4.2 Reverberation time in non-diffuse rooms 94
4.5 Measurement of reverberation time 96
References 98
5 Introduction to sound insulation 101
5.1 Airborne sound insulation 101
5.1.1 The sound transmission loss 101
5.1.2 Sound insulation of a partition between
two rooms 102
5.1.3 Measurement of sound insulation 103
5.1.4 Multi-element partitions and apertures 104
5.2 Single leaf constructions 106
5.2.1 Sound transmission through a solid material 106
5.2.2 The mass law 109
5.2.3 Sound insulation at random incidence 111
5.2.4 The critical frequency 112
5.2.5 A simple model of sound insulation
of single constructions 113
5.2.6 Examples of single constructions 116
5.3 Double leaf constructions 121
5.3.1 Impedance model for sound transmission 121
5.3.2 The mass-air-mass resonance frequency 123
5.3.3 Sound insulation of double constructions 124
5.3.4 Examples of double constructions 125
5.4 Slits and leaks 128
5.5 Flanking transmission 131
5.6 Enclosures 135
5.7 Impact sound insulation 136
5.7.1 Impact sound pressure level 136
5.7.2 Historical note 138
5.7.3 Sum of airborne and impact sound insulation 138
5.8 Single-number rating of sound insulation 140
viii Contents
5.8.1 Weighted sound reduction index and
the sound transmission class 140
5.8.2 Weighted impact sound pressure level and
the impact insulation class 142
5.8.3 Alternative reference curve for evaluating
the impact sound insulation 144
5.8.4 Previous methods for rating sound insulation 145
5.8.5 Historical note 145
5.8.6 Spectrum adaptation terms 146
5.9 Requirements for sound insulation 150
References 151
6 Sound radiation from plates 155
6.1 Normal modes in a rectangular plate 155
6.2 Sound radiation from a propagating transverse wave 160
6.3 The radiation efficiency 163
6.4 Sound radiation calculated by Rayleigh’s method 164
6.5 Sound radiation from forced vibrations
in a rectangular plate 166
6.5.1 Approximate results 171
6.6 Sound radiation from supersonic bending waves 174
6.7 Sound radiation from resonant
vibrations in a rectangular plate 174
6.7.1 Approximate results 179
6.7.2 Directivity of resonant radiation 181
6.7.3 Combined forced and resonant radiation 183
6.8 The refraction effect 184
References 187
7 Statistical energy analysis, SEA 189
7.1 Energy balance in a resonant system 189
7.2 Coupling between resonant systems 191
7.3 Resonant transmission through a single wall 194
7.4 Forced and resonant transmission through a single wall 197
7.5 Acoustic excitation of resonant vibrations in a plate 198
7.5.1 Excitation from one side 198
7.5.2 Freely hung plate in a room 199
7.6 Resonant transmission through a slab with extended area 199
References 201
Contents ix
8 Airborne sound transmission through single constructions 203
8.1 Sound insulation of homogeneous,
isotropic plates at random incidence 203
8.1.1 Total transmitted sound power 203
8.1.2 The mass law 204
8.1.3 Wall impedance 205
8.1.4 The loss factor 210
8.1.5 Forced transmission 211
8.1.6 Resonant transmission 214
8.1.7 Total transmission: a calculation model 215
8.2 Sound insulation of acoustically thick plates 218
8.3 Sound insulation at very low frequencies 221
8.4 Sound insulation of subdivided structures 224
8.5 Sound insulation at oblique incidence 226
8.5.1 Definition of external transmission loss 226
8.5.2 Transmission from outside to inside 227
8.5.3 Transmission from inside to outside 228
8.5.4 External transmission loss for
a single construction 228
8.6 Orthotropic plates 229
8.7 Sandwich plates 234
8.7.1 Speed of transverse waves 234
8.7.2 Resonant transmission 238
8.7.3 Forced transmission 240
8.7.4 Dilatational resonance 240
References 244
9 Airborne sound transmission through
double constructions 247
9.1 Transmission via the cavity 247
9.1.1 Normal incidence of sound 247
9.1.2 The resonance frequency 249
9.1.3 Standing waves in the cavity 250
9.1.4 Calculation for random incidence 250
9.1.5 Weakly attenuated cavity 252
9.2 Transmission via sound bridges 254
9.2.1 Point connections 255
9.2.2 Line connections 257