Sound insulation

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Sound Insulation

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Sound Insulation

Carl Hopkins

AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD

PARIS • SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO

Butterworth-Heinemann is an imprint of Elsevier

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First edition 2007

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Preface

The most effective approach to sound insulation design involves the use of measured data

along with statistical and/or analytical models, blended with a combination of empiricism, expe￾rience, and pragmatism. Engineering design is predominantly experiential in nature; applying

past experience to new problems. This often impedes rapid progress when applying a general

knowledge of acoustics to a specific area such as sound insulation. This book is intended for

students, engineers, consultants, building designers, researchers and those involved in the

manufacture and design of building products. It uses theory and measurements to explain

concepts that are important for the application, interpretation and understanding of guidance

documents, test reports, product data sheets, published papers, regulations, and Standards.

The intention is to enable the reader to tackle many different aspects of sound insulation by

providing a textbook and a handbook within a single cover. Readers with a background in

acoustics can jump straight to the topic of interest in later chapters and, if needed, return to

earlier chapters for fundamental aspects of the theory. This book draws on a wealth of pub￾lished literature that is relevant to sound insulation, but it does not document a historical review

of every incremental step in its development, or cover all possible approaches to the prediction

of sound transmission. The references will provide many starting points from which the reader

can dive into the vast pool of literature themselves.

All prediction models and measurement methods have their limitations, but with knowledge of

their strengths and weaknesses it becomes much easier to make design decisions and to find

solutions to sound insulation problems. A model provides more than just a procedure for calcu￾lating a numerical result. The inherent assumptions should not simply be viewed as limitations

from which use of the model is quickly dismissed; the assumptions may well shed light on a

solution to the problem at hand. The fact that we need to deal with a relatively wide frequency

range in building acoustics means that there is no single theoretical approach that is suitable

for all problems. We rarely know all the variables; but the simple models often identify the ones

which are most important. A model provides no more than the word implies; in this sense, every

model is correct within the confines of its assumptions. The models and theories described in

this book have been chosen because of the insight they give into the sound transmission pro￾cess. There are many different approaches to the prediction of sound transmission. In general,

the more practical theories are included and these will provide the necessary background for

the reader to pursue more detailed and complex models when required. Occasionally a more

complex theory is introduced but usually with the intention of showing that a simpler method

may be adequate. Choosing the most accurate and complex model for every aspect of sound

transmission is unnecessary. There are so many transmission paths between two rooms in a

building that decisions can often be made whilst accepting relatively high levels of uncertainty

in the less important transmission paths. Before doing any calculations it is worth pausing for a

second to picture the scene at the point of construction. The uncertainty in describing a building

construction tends to differ between walls, floors, or modular housing units that are produced

on a factory assembly line compared with a building site that is exposed to the weather and

a wide range in the quality of workmanship. Uncertainty is often viewed rather negatively as

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Preface

being at the crux of all design problems, but uncertainty in the form of statistics and probability

is part of many theoretical solutions for the transmission of sound and vibration in built-up

structures. To avoid sound insulation problems in a completed building, uncertainty needs to

be considered at an early stage in the design process. In the words of Francis Bacon (Philoso￾pher, 1561–1626) “If a man will begin with certainties, he shall end in doubts, but if he will be

content to begin with doubts, he shall end in certainties’’.

Sound not only travels via direct transmission across the separating wall or floor, but via

the many other walls and floors, as well as via other building elements such as cavities,

ceiling voids, and beams; we refer to this indirect transmission as flanking transmission. To

predict both direct and flanking transmission, statistical models based upon Statistical Energy

Analysis (SEA) are particularly practical because they tend to make gross assumptions about

the building elements. This is important because specific details on the material properties and

dimensions are not always available in the early (and sometimes late) stages of the design. In

fact, during the construction phase a variety of similar building products are often substituted

for the one that was originally specified. In addition the quality of workmanship can be highly

variable within a single building, let alone between different buildings. SEA or SEA-based

models allow an assessment of the different sound transmission paths to determine which

paths are likely to be of most importance. These models are also attractive because labora￾tory sound insulation measurements of complex wall or floor elements can be incorporated

into the models. Some construction elements or junction details are not well suited to SEA

or SEA-based models. Analytical models and finite element methods therefore have a role to

play, although they tend to be more orientated to research work due to the time involved in

creating and validating each model. Engineers involved in laboratory measurements become

painfully aware that significant changes in the sound insulation can sometimes be produced

by small changes to the test element (such as extra screws, different layouts for the frame￾work, or different positions for the porous material in the cavity). Hypersensitivity to certain

changes in the construction can often be explained using statistical or deterministic models;

but the latter may be needed to help gain an insight into the performance of one specific test

element.

Sound insulation tends to be led by regulations, where the required performance is almost

always described using a single integer number in decibels. It is common to draw a ‘line in the

sand’ for an acceptable level of sound insulation, such that if the construction fails to achieve

this by one decibel, the construction is deemed to have failed. This needs to be considered in

the context of a specific pair of rooms in one specific building; we can rarely predict the sound

insulation in a specific situation to plus or minus one decibel. However, we can often make

reasonable estimates of the average sound insulation for a large number of nominally identical

constructions. The design process must therefore consider the sound insulation that can be

provided on average, as well as the performance of individual constructions on a particular site.

The fact that we need to design and predict the sound insulation in the field on a statistical

basis does not mean that we can accept low precision measurements; quite the opposite.

Every decibel is important to the builder having the sound insulation measured to check that

the building satisfies the regulations; to the manufacturer who wants to claim an advantage

over a competitor’s product; to the engineer trying to assess sound transmission mechanisms

with laboratory measurements; to the designer trying to choose between two different building

products, and to the house builder trying to reduce costs by avoiding over specification in the

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Preface

design. It is important to keep in perspective those situations where the highest level of accuracy

is necessary, along with those situations where a rough estimate is more than sufficient. The

intention is to provide the reader with a background from which they can decide the appropriate

level for the problem at hand. In an engineering context the words ‘reasonable’ and ‘adequate’

will quite often be used to describe equations, prediction models, assumptions, and rules of

thumb.

Overview of contents

Chapters 1 and 2 deal with theoretical aspects of sound fields in spaces and vibration fields

on structures. Sound transmission in buildings is fundamentally concerned with the coupling

between these fields. For the reader who is relatively new to acoustics it should be sufficient

to start these chapters with a basic background in acoustics terminology, wave theory, and

room acoustics. It is assumed that the reader has more experience in room acoustics, or is

perhaps more comfortable with these concepts. Sound and vibration are discussed in a similar

style so that the reader can see the similarities, and the many differences, between them. The

layout of these chapters is intended to simplify its use as a handbook when solving problems

that are specific to room acoustics, vibration in buildings, and sound insulation. Sound and

vibration fields are described in terms of both waves and modes. It is useful to be able to think

in terms of waves and modes interchangeably, taking the most convenient approach to solve

the problem at hand.

Chapter 3 looks at sound and vibration measurements relating to sound insulation and material

properties. This chapter deals with the underlying theory behind the measurements, and the

reasons for adopting different measurement methods. This chapter forms a bridge between

the sound and vibration theory in Chapters 1 and 2 and the prediction of sound insulation in

Chapters 4 and 5. However, it is not possible to explain all aspects of measurements without

referring to some of the theory in Chapters 4 and 5. Some readers may choose to start the

book in Chapter 3 and it will sometimes be necessary to refer forward as well as back.

Chapter 4 looks at direct sound transmission across individual building elements. Sound and

vibration theory from Chapters 1 and 2 is combined with material property measurements from

Chapter 3 to look at prediction models for different sound transmission mechanisms. There is no

single theoretical model that can deal with all aspects of sound insulation. Many constructions

are so complex that reliance is ultimately placed on measurements. The aim of this chapter is

to give insight and understanding into sound transmission for relatively simple constructions.

These form a basis from which measurement, prediction, and design decisions can be tackled

on more complex constructions. The chapter is based around prediction using SEA augmented

by classical theories based on infinite plates. Some aspects of sound transmission are not

suitable for SEA models, but the SEA framework can conveniently be used to highlight these

areas such that other models can be sought.

Chapter 5 concerns sound insulation in situ where there is both direct and flanking transmission.

Prediction of vibration transmission across idealized plate junctions is used to illustrate issues

that are relevant to measurement and prediction with other types of plates and more complex

junction connections. Following on from Chapter 4 the application of SEA is extended to the

prediction of direct and flanking transmission. In addition, a simplification of SEA results in an

SEA-based model that facilitates the inclusion of laboratory sound insulation measurements.

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Preface

Generalizations

In building acoustics the main frequency range used to assess sound insulation lays between

the 100 and 3150 Hz one-third-octave-bands; an optional extended frequency range is defined

between the 50 and 5000 Hz one-third-octave-bands. In this book the range between 50 and

5000 Hz will be referred to as the building acoustics frequency range. For sound and vibration

in buildings, it is possible to describe many general trends by defining the low-, mid-, and

high-frequency ranges using one-third-octave-band centre frequencies as follows:

• Low-frequency range : 50–200 Hz.

• Mid-frequency range : 250–1000 Hz.

• High-frequency range : 1250–5000 Hz.

The only exact boundaries in these ranges correspond to the 50 and 5000 Hz bands; the

intermediate boundaries need to be considered with a degree of flexibility; usually within plus

or minus one-third-octave-band.

It is also useful to try and define a range of room volumes that are typically encountered in

buildings. For the purpose of making general statements it will be assumed that ‘typical rooms’

have volumes between 20 and 200 m3; this covers the majority of practical situations.

Constructions throughout the world are primarily built with concrete, masonry, timber, steel,

glass and plasterboard. In a very general sense, the term ‘heavyweight’ is used for con￾crete, masonry, and heavy-steel elements and ‘lightweight’ is used for timber, glass,

plasterboard, and light-steel elements. There are also combinations that form a separate

lightweight/heavyweight category, such as timber floors with a surface layer of concrete screed.

For generic and proprietary materials that are commonly used in lightweight and heavyweight

constructions, material properties, and sound insulation values are included in this book to

help the reader get a feel for realistic values and to assess general trends.

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Contents

Acknowledgements xix

List of symbols xxi

1. Sound fields

1.1 Introduction 1

1.2 Rooms 1

1.2.1 Sound in air 1

1.2.1.1 Complex notation 3

1.2.1.2 Plane waves 4

1.2.1.3 Spherical waves 6

1.2.1.4 Acoustic surface impedance and admittance 7

1.2.1.5 Decibels and reference quantities 8

1.2.1.6 A-weighting 9

1.2.2 Impulse response 10

1.2.3 Diffuse field 11

1.2.3.1 Mean free path 12

1.2.4 Image sources 15

1.2.4.1 Temporal density of reflections 15

1.2.5 Local modes 17

1.2.5.1 Modal density 19

1.2.5.2 Mode count 22

1.2.5.3 Mode spacing 23

1.2.5.4 Equivalent angles 24

1.2.5.5 Irregularly shaped rooms and scattering objects 24

1.2.6 Damping 26

1.2.6.1 Reflection and absorption coefficients 27

1.2.6.2 Absorption area 29

1.2.6.3 Reverberation time 29

1.2.6.3.1 Diffuse field 31

1.2.6.3.2 Non-diffuse field: normal mode theory 34

1.2.6.3.3 Non-diffuse field: non-uniform distribution of absorption 41

1.2.6.4 Internal loss factor 42

1.2.6.5 Coupling loss factor 42

1.2.6.6 Total loss factor 42

1.2.6.7 Modal overlap factor 42

1.2.7 Spatial variation in sound pressure levels 44

1.2.7.1 Sound fields near room boundaries 45

1.2.7.1.1 Perfectly reflecting rigid boundaries 45

1.2.7.1.2 Other boundary conditions 51

1.2.7.2 Sound field associated with a single mode 52

1.2.7.3 Excitation of room modes 56

1.2.7.4 Diffuse and reverberant fields 57

1.2.7.5 Energy density 59

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1.2.7.5.1 Diffuse field 59

1.2.7.5.2 Reverberant sound fields with non-exponential

decays 61

1.2.7.6 Direct sound field 62

1.2.7.7 Decrease in sound pressure level with distance 62

1.2.7.8 Sound fields in frequency bands 65

1.2.7.8.1 Below the lowest mode frequency 65

1.2.7.8.2 Reverberant field: below the Schroeder cut-off

frequency 66

1.2.7.8.3 Reverberant field: at and above the Schroeder cut-off

frequency 70

1.2.7.9 Statistical description of the spatial variation 71

1.2.8 Energy 75

1.2.8.1 Energy density near room boundaries: Waterhouse correction 76

1.3 Cavities 77

1.3.1 Sound in gases 77

1.3.2 Sound in porous materials 78

1.3.2.1 Characterizing porous materials 79

1.3.2.1.1 Porosity 79

1.3.2.1.2 Airflow resistance 80

1.3.2.1.3 Fibrous materials 81

1.3.2.2 Propagation theory for an equivalent gas 82

1.3.3 Local modes 87

1.3.3.1 Modal density 87

1.3.3.2 Equivalent angles 89

1.3.4 Diffuse field 90

1.3.4.1 Mean free path 92

1.3.5 Damping 92

1.3.5.1 Reverberation time 92

1.3.5.2 Internal losses 92

1.3.5.2.1 Sound absorption coefficient: Locally reacting porous

materials 94

1.3.5.3 Coupling losses 96

1.3.5.4 Total loss factor 96

1.3.5.5 Modal overlap factor 96

1.3.6 Energy 97

1.4 External sound fields near building façades 97

1.4.1 Point sources and semi-infinite façades 97

1.4.1.1 Effect of finite reflector size on sound pressure levels near the façade 101

1.4.1.2 Spatial variation of the surface sound pressure level 102

1.4.2 Line sources 104

References 107

2. Vibration fields

2.1 Introduction 111

2.2 Vibration 111

2.2.1 Decibels and reference quantities 112

2.3 Wave types 112

2.3.1 Quasi-longitudinal waves 114

2.3.1.1 Thick plate theory 117

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2.3.2 Transverse waves 118

2.3.2.1 Beams: torsional waves 118

2.3.2.2 Plates: transverse shear waves 121

2.3.3 Bending waves 123

2.3.3.1 Thick beam/plate theory 133

2.3.3.2 Orthotropic plates 135

2.3.3.2.1 Profiled plates 136

2.3.3.2.2 Corrugated plates 139

2.3.3.2.3 Ribbed plates 139

2.4 Diffuse field 140

2.4.1 Mean free path 140

2.5 Local modes 141

2.5.1 Beams 141

2.5.1.1 Bending waves 142

2.5.1.2 Torsional waves 144

2.5.1.3 Quasi-longitudinal waves 145

2.5.1.4 Modal density 145

2.5.2 Plates 148

2.5.2.1 Bending waves 149

2.5.2.2 Transverse shear waves 149

2.5.2.3 Quasi-longitudinal waves 150

2.5.2.4 Modal density 150

2.5.3 Equivalent angles 152

2.6 Damping 154

2.6.1 Structural reverberation time 154

2.6.2 Absorption length 156

2.6.3 Internal loss factor 157

2.6.4 Coupling loss factor 158

2.6.5 Total loss factor 159

2.6.6 Modal overlap factor 159

2.7 Spatial variation in vibration level: bending waves on plates 160

2.7.1 Vibration field associated with a single mode 160

2.7.2 Nearfields near the plate boundaries 161

2.7.3 Diffuse and reverberant fields 167

2.7.4 Reverberant field 167

2.7.5 Direct vibration field 168

2.7.6 Statistical description of the spatial variation 172

2.7.7 Decrease in vibration level with distance 173

2.8 Driving-point impedance and mobility 178

2.8.1 Finite plates (uncoupled): Excitation of local modes 181

2.8.2 Finite plates (coupled): Excitation of global modes 182

2.8.3 Infinite beams and plates 185

2.8.3.1 Excitation in the central part 185

2.8.3.2 Excitation at the edge 189

2.8.3.3 Finite beams and plates with more complex cross-sections 189

2.9 Sound radiation from bending waves on plates 197

2.9.1 Critical frequency 197

2.9.2 Infinite plate theory 198

2.9.3 Finite plate theory: Radiation from individual bending modes 202

2.9.4 Finite plate theory: Frequency-average radiation efficiency 209

2.9.4.1 Method No. 1 209

2.9.4.2 Method No. 2 210

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2.9.4.3 Method No. 3 (masonry/concrete plates) 212

2.9.4.4 Method No. 4 (masonry/concrete plates) 212

2.9.4.5 Plates connected to a frame 213

2.9.5 Radiation into a porous material 213

2.9.6 Radiation into the soil 214

2.9.7 Nearfield radiation from point excitation 214

2.10 Energy 217

References 217

3. Measurement

3.1 Introduction 221

3.2 Transducers 221

3.2.1 Microphones 221

3.2.2 Accelerometers 222

3.2.2.1 Mounting 223

3.2.2.2 Mass loading 223

3.3 Signal processing 224

3.3.1 Signals 224

3.3.2 Filters 227

3.3.2.1 Bandwidth 227

3.3.2.2 Response time 230

3.3.3 Detector 230

3.3.3.1 Temporal averaging 230

3.3.3.2 Statistical description of the temporal variation 232

3.4 Spatial averaging 234

3.4.1 Spatial sampling of sound fields 235

3.4.1.1 Stationary microphone positions 235

3.4.1.2 Continuously moving microphones 237

3.4.2 Measurement uncertainty 238

3.5 Airborne sound insulation 239

3.5.1 Laboratory measurements 239

3.5.1.1 Sound intensity 242

3.5.1.1.1 Low-frequency range 243

3.5.1.2 Improvement of airborne sound insulation due to wall linings,

floor coverings, and ceilings 245

3.5.1.2.1 Airborne excitation 245

3.5.1.2.2 Mechanical excitation 245

3.5.1.3 Transmission suites 246

3.5.1.3.1 Suppressed flanking transmission 247

3.5.1.3.2 Total loss factor 249

3.5.1.3.3 Niche effect 253

3.5.2 Field measurements within buildings 258

3.5.2.1 Reverberation time 260

3.5.2.2 Sound intensity 261

3.5.3 Field measurements of building façades 262

3.5.3.1 Sound insulation of building elements 262

3.5.3.1.1 Loudspeaker method 262

3.5.3.1.2 Sound intensity 264

3.5.3.1.3 Road traffic method 266

3.5.3.1.4 Aircraft and railway noise 266

3.5.3.2 Sound insulation of façades 267

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3.5.4 Other measurement issues 268

3.5.4.1 Background noise correction 268

3.5.4.2 Converting to octave-bands 270

3.5.4.3 Comparing the airborne sound insulation measured using

sound pressure and sound intensity 270

3.5.4.4 Variation in the sound insulation of an element due to moisture

content and drying time 271

3.5.4.5 Identifying sound leaks and airpaths 271

3.6 Impact sound insulation (floors and stairs) 272

3.6.1 Laboratory measurements 273

3.6.1.1 Improvement of impact sound insulation due to floor

coverings 273

3.6.1.1.1 Heavyweight base floor (ISO) 274

3.6.1.1.2 Lightweight base floors (ISO) 274

3.6.2 Field measurements 275

3.6.3 ISO tapping machine 275

3.6.3.1 Force 276

3.6.3.2 Power input 283

3.6.3.3 Issues arising from the effect of the ISO tapping machine

hammers 284

3.6.3.4 Modifying the ISO tapping machine 291

3.6.3.5 Rating systems for impact sound insulation 292

3.6.3.6 Concluding discussion 297

3.6.4 Heavy impact sources 298

3.6.5 Other measurement issues 301

3.6.5.1 Background noise correction 301

3.6.5.2 Converting to octave-bands 301

3.6.5.3 Time dependency 301

3.6.5.4 Dust, dirt, and drying time 303

3.6.5.5 Size of test specimen 303

3.6.5.6 Static load 303

3.6.5.7 Excitation positions 305

3.7 Rain noise 305

3.7.1 Power input 305

3.7.2 Radiated sound 311

3.7.3 Other measurement issues 311

3.8 Reverberation time 313

3.8.1 Interrupted noise method 313

3.8.2 Integrated impulse response method 314

3.8.3 Influence of the signal processing on the decay curve 318

3.8.3.1 Effect of the detector 318

3.8.3.2 Effect of the filters 321

3.8.3.2.1 Forward-filter analysis 322

3.8.3.2.2 Reverse-filter analysis 326

3.8.4 Evaluation of the decay curve 327

3.8.5 Statistical variation of reverberation times in rooms 329

3.9 Maximum Length Sequence (MLS) measurements 333

3.9.1 Overview 334

3.9.2 Limitations 339

3.9.2.1 Temperature 340

3.9.2.2 Air movement 341

3.9.2.3 Moving microphones 341

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3.10 Sound intensity 342

3.10.1 p–p sound intensity probe 344

3.10.1.1 Sound power measurement 346

3.10.1.1.1 Measurement surfaces 346

3.10.1.1.2 Discrete point and scanning measurements 347

3.10.1.2 Error analysis 348

3.11 Properties of materials and building elements 353

3.11.1 Airflow resistance 353

3.11.2 Sound absorption 354

3.11.2.1 Standing wave tube 354

3.11.2.2 Reverberation room 354

3.11.3 Dynamic stiffness 355

3.11.3.1 Resilient materials used under floating floors 356

3.11.3.1.1 Measurement 357

3.11.3.1.2 Calculation of dynamic stiffness 359

3.11.3.2 Wall ties 361

3.11.3.2.1 Measurement 361

3.11.3.2.2 Calculation of dynamic stiffness 364

3.11.3.3 Structural reverberation time 364

3.11.3.4 Internal loss factor 365

3.11.3.5 Quasi-longitudinal phase velocity 367

3.11.3.6 Bending phase velocity 370

3.11.3.7 Bending stiffness 371

3.11.3.8 Driving-point mobility 371

3.11.3.9 Radiation efficiency 373

3.12 Flanking transmission 375

3.12.1 Flanking laboratories 376

3.12.1.1 Suspended ceilings and access floors 376

3.12.1.2 Other flanking constructions and test junctions 377

3.12.2 Ranking the sound power radiated from different surfaces 380

3.12.2.1 Vibration measurements 380

3.12.2.2 Sound intensity 380

3.12.3 Vibration transmission 384

3.12.3.1 Structural intensity 384

3.12.3.1.1 a–a structural intensity probe 388

3.12.3.1.2 Structural power measurement 389

3.12.3.1.3 Error analysis 390

3.12.3.1.4 Visualizing net energy flow 391

3.12.3.1.5 Identifying construction defects 395

3.12.3.2 Velocity level difference 396

3.12.3.2.1 Stationary excitation signal and fixed power input 397

3.12.3.2.2 Impulse excitation 398

3.12.3.2.3 Excitation and accelerometer positions 400

3.12.3.3 Coupling Loss Factor, ηij 400

3.12.3.4 Vibration Reduction Index, Kij 402

References 402

4. Direct sound transmission

4.1 Introduction 409

4.2 Statistical energy analysis 409

xiv