Room Acoustics Room Acoustics Fourth edition Heinrich Kuttruff Institut für Technische Akustik, Technische Hochschule Aachen, Aachen, Germany First published 1973 by Elsevier Science Publishers Ltd Second edition 1979 Third edition 1991 Fourth edition published 2000 by Spon Press 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by Spon Press 29 West 35th Street, New York, NY 10001 This edition published in the Taylor & Francis e-Library, 2001. Spon Press is an imprint of the Taylor & Francis Group © 1973, 1979, 1991 Elsevier Science Publishers; 1999, 2000 Heinrich Kuttruff The right of Heinrich Kuttruff to be identified as the Author of this Work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988 All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Kuttruff, Heinrich. Room acoustics/Heinrich Kuttruff.–4th ed. p. cm. Includes bibliographical references and index. 1. Architectural acoustics. I. Title. NA2800 .K87 2000 729′.29–dc21 00-021584 ISBN 0-419-24580-4 (Print Edition) ISBN 0-203-18623-0 Master e-book ISBN ISBN 0-203-18746-6 (Glassbook Format) Contents Preface to the fourth edition ix Preface to the first edition xi Introduction 1 1 Some facts on sound waves, sources and hearing 6 1.1 Basic relations, the wave equation 6 1.2 Plane waves and spherical waves 8 1.3 Energy density and radiation intensity 13 1.4 Signals and systems 15 1.5 Sound pressure level and sound power level 20 1.6 Some properties of human hearing 21 1.7 Sound sources 24 References 30 2 Reflection and scattering 31 2.1 Reflection factor, absorption coefficient and wall impedance 32 2.2 Sound reflection at normal incidence 33 2.3 Sound reflection at oblique incidence 36 2.4 A few examples 39 2.5 Random sound incidence 46 2.6 Scattering, diffuse reflection 51 References 58 3 The sound field in a closed space (wave theory) 59 3.1 Formal solution of the wave equation 60 3.2 Normal modes in rectangular rooms with rigid boundaries 64 3.3 Non-rigid walls 71 vi Contents 3.4 Steady state sound field 75 3.5 Decaying modes, reverberation 82 References 88 4 Geometrical room acoustics 89 4.1 Enclosures with plane walls, image sources 90 4.2 The temporal distribution of reflections 97 4.3 The directional distribution of reflections, diffusion 102 4.4 Enclosures with curved walls 105 4.5 Enclosures with diffusely reflecting walls 110 References 114 5 Reverberation and steady state energy density 115 5.1 Basic properties and realisation of diffuse sound fields 116 5.2 Mean free path and average rate of reflections 122 5.3 Sound decay and reverberation time 126 5.4 The influence of unequal path lengths 130 5.5 Enclosure driven by a sound source 133 5.6 Enclosures with diffusely reflecting walls 137 5.7 Coupled rooms 142 References 145 6 Sound absorption and sound absorbers 147 6.1 The attenuation of sound in air 147 6.2 Unavoidable wall absorption 150 6.3 Sound absorption by vibrating or perforated boundaries 151 6.4 Extended resonance absorbers 154 6.5 Helmholtz resonators 159 6.6 Sound absorption by porous materials 163 6.7 Audience and seat absorption 173 6.8 Miscellaneous objects (freely hanging fabrics, pseudostochastic diffusers, etc.) 180 6.9 Anechoic rooms 184 References 187 7 Characterisation of subjective effects 189 7.1 Some general remarks on reflections and echoes 193 7.2 The perceptibility of reflections 196 7.3 Echoes and colouration 199 7.4 Early energy: definition, clarity index, speech transmission index 207 7.5 Reverberation and reverberance 213 Contents vii 7.6 Sound pressure level, strength factor 221 7.7 Spaciousness of sound fields 222 7.8 Assessment of concert hall acoustics 226 References 231 8 Measuring techniques in room acoustics 234 8.1 General remarks on instrumentation 235 8.2 Measurement of the impulse response 237 8.3 Correlation measurement 244 8.4 Examination of the time structure of the impulse response 248 8.5 Measurement of reverberation 254 8.6 Sound absorption – tube methods 260 8.7 Sound absorption – reverberation chamber 265 8.8 Diffusion 268 References 276 9 Design considerations and design procedures 277 9.1 Direct sound 278 9.2 Examination of the room shape with regard to reflections 280 9.3 Reverberation time 286 9.4 Prediction of noise level 293 9.5 Acoustical scale models 297 9.6 Computer simulation 300 9.7 Auralisation 306 References 308 10 Electroacoustic installations in rooms 310 10.1 Loudspeaker directivity 311 10.2 Design of electroacoustic systems for speech transmission 316 10.3 A few remarks on the selection of loudspeaker positions 319 10.4 Acoustical feedback and its suppression 323 10.5 Reverberation enhancement with external reverberators 330 10.6 Reverberation enhancement by controlled feedback 337 References 342 Index 343 Preface to the fourth edition Almost a decade has elapsed since the third edition and during this period many new ideas and methods have been introduced into room acoustics. I therefore welcome the opportunity to prepare a new edition of this book and to include the more important of those developments, while also intro- ducing new topics which were not dealt with in earlier editions. In room acoustics, as in many other technical fields, the digital computer has continued its triumphant progress; nowadays hardly any acoustical measurements are carried out without using a computer, allowing previ- ously inconceivable improvements in accuracy and rapidity. Therefore, an update of the chapter on measuring techniques (Chapter 8) was essential. Furthermore, the increased availability of computers has opened new ways for the computation and simulation of sound fields in enclosures. These have led to better and more reliable methods in the practical design of halls; indeed, due to its flexibility and low cost, sound field simulation will prob- ably replace the conventional scale model in the near future. Moreover, by simulation it can demonstrated what a new theatre or concert hall which is still on the drawing board will sound like when completed (‘auralisation’). These developments are described in Chapter 9, which contains a separate section on auralisation. Also included in the new edition are sections on sound scattering and diffuse reflection, on sound reflection from curved walls, on sound absorp- tion by several special arrangements (freely hanging porous material, Schroeder diffusers) and on the measurement of diffuse reflections from walls. As in the earlier editions, no attempt is made to list all relevant publica- tions on room acoustics, and references are given only where I have adopted material from another publication, or to enable the reader to obtain more detailed information on a particular topic. I apologise for leaving many important and interesting publications unmentioned. The preparation of a new edition offered the chance to present some subjects in a more comprehensive and logical way, to improve numerous text passages and formulae and to correct errors and mistakes that inevit- ably crept into the previous editions. I appreciate the suggestions of many