ACOUSTICS ACOUSTICS Leo L. Beranek 1954 Edition Acoustic Laboratory Massachusetts Institute of Technology Bolt Beranek and Newman, Inc. 1993 Edition 975 Memorial Drive, Suite 804 Cambridge, MA 02138 Library of Congress Catalog Card Number: 86-70671 International Standard Book Number: 0-88318-494-X Copyright© 1954, 1986, 1990, 1993, 1996, by the Acoustical Society of America All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means (electronic, mechanical, photocopying, recording, or otherwise) without the prior written permission of the publisher. Published by the Acoustical Society of America through the American Institute of Physics, Inc. 500 Sunnyside Blvd., Woodbury, New York 11797 Printed in the United States of America PREFACE Acoustics is a most fascinating subject. Music, architecture, engineer­ ing, science, drama, medicine, psychology, and linguistics all seek from it answers to basic questions in their fields. In the Acoustics Laboratory at M.I.T. students may be found working on such diversified problems as auditorium and studio design, loudspeaker design, subjective percep­ tion of complex sounds, production of synthetic speech, propagation of sound in the atmosphere, dispersion of sound in liquids, reduction of noise from jet-aircraft engines, and ultrasonic detection of brain tumors. The annual meetings of the Acoustical Society of America are veritable five- ring shows, with papers and symposia on subjects in all the above-named fields. Opportunities for employment are abundant today because man­ agement in industry has recognized the important contributions that acoustics makes both to the improvement of their products and to the betterment of employee working conditions. There is no easy road to an understanding of present-day acoustics. First the student must acquire the vocabulary that is peculiar to the subject. Then he must assimilate the laws governing sound propagation and sound radiation, resonance, and the behavior of transducers in an acoustic medium. Last, but certainly not of least importance, he must learn to understand the hearing characteristics of people and the reac­ tions of listeners to sounds and noises. This book is the outgrowth of a course in acoustics that the author has taught to seniors and to first-year graduate students in electrical engineering and communication physics. The basic wave equation and some of its more interesting solutions are discussed in detail in the first part of the text. The radiation of sound, components of acoustical sys­ tems, microphones, loudspeakers, and horns are treated in sufficient detail to allow the serious student to enter into electroacoustical design. There is an extensive treatment of such important problems as sound in enclosures, methods for noise reduction, hearing, speech intelligibility, and psychoacoustic criteria for comfort, for satisfactory speech intelligi­ bility, and for pleasant listening conditions. The book differs in one important respect from conventional texts on acoustics in that it emphasizes the practical application of electrical- circuit theory in the solution of a wide variety of problems. Wherever possible, the background of the electrical engineer and the communica­ tion physicist is utilized in explaining acoustical concepts. vi PREFACE The high-fidelity expert will find the chapters on loudspeaker enclosures, horns, and rooms particularly interesting because they show how the per­ formance of loudspeakers either in baffles or attached to horns may be accurately and simply calculated. These chapters also illustrate the necessity of considering in design the over-all system, including the amplifier, the loudspeaker, the baffle or horn and considering also the room in which they are to be operated. Numerical examples and sum­ mary charts are given to facilitate application of this material to music- reproduction systems. In view of the increased interest in noise control, the author has kept this subject in mind in writing Chapters 1, 2, 4, and 10 to 13. These chapters served as the basis of a special summer program on noise reduction at M.I.T. in 1953. The material of Chapters 11 and 13 is new, and it is hoped that it will be of value to those interested in noise and its effect on human beings. In short, the engineer or scientist who wishes to practice in the field of acoustics and who does not intend to confine his efforts to theoretical matters must know the material of this text. Problems for each chapter are included at the end of the text for use by the student. References to collateral reading in English are given in the text, although no attempt has been made to give a bibliography of the primary sources of material. Suggestions to instructors for best use of the text are given immediately after this preface. The author wishes to express his deep appreciation to Francis M. Wiener and Rudolph H. Nichols, Jr., for their assistance in the detailed review and editing of the text and the preparation of some original material. Many members of the Acoustics Laboratory at M.I.T. have read one or more chapters and have given valuable assistance to the author. Of these, particular mention is made of Mary Anne Summer- field, Walter A. Rosenblith, Kenneth N. Stevens, Jerome R. Cox, Jordan J. Baruch, Joanne J. English, and Norman Doelling. The illustrations are due to the highly capable and untiring efforts of Clare Twardzik. The author is deeply indebted to his typist, Elizabeth H. Jones, to his secretary, Lydia Bonazzoli, and to his wife, Phyllis, who made it possible for him to complete the text within a reasonably short span of time. Leo L. Beranek SUGGESTIONS FOR INSTRUCTORS This text is divided into thirteen chapters, comprising thirty-two parts. Each part is intended to be approximately 1 week’s work, although this will vary among students owing to differences in their previous training. If the entire class expects to take a full year of acoustics, the parts should be taught in sequence, with the exception of Part XXVIII, Meas­ urement of Acoustic Levels, which may be referred to in associated labo­ ratory experiments and demonstrations throughout the course. If only a part of the class plans to continue through both terms, the fundamental material should be taught in the first term and the more applied material in the second. One suggested division, in this case, is as follows: First Term Second Term Part I. Introduction Fart V. Energy Density and Intensity Part 11. Terminology Part IX. Circuit Theorems, Part III. The Wave Equa­ Energy and Power tion Part XI. Directivity Index Part IV. Solutions of the and Directivity Wave Equation Factor Part XIV. General Character­ Part VI. Mechanical Cir­ istics of Micro­ cuits phones Part VII. Acoustical Part XV. Pressure Circuits Microphones Part VIII. Transducers Part XVI. Gradient and Com­ bination Micro­ Part X. Directivity Patterns phones Part XVIII. Design Factors Af­ Part XII. Radiation Imped­ fecting Direct-radi­ ances ator Loudspeakers Part XIII. Acoustic Part XX. Bass Reflex Enclo­ Elements sures Part XVII. Basic Theory of Part XXI. Horn Driving Direct-radiator Units Loudspeakers Part XXII. Horns vii viii SUGGESTIONS FOR INSTRUCTORS First Term Second Term Part XIX. Simple Enclosures Part XXV. Sound Transmis­ sion through Walls Part XXIII. Sound Fields in between Enclosures Small Regularly Part XXVI. Noise Control Pro­ Shaped Enclosures cedures and Noise Sources Part XXVII. Acoustic Transmis­ Part XXIV. Sound Fields in sion Paths Large Irregularly Part XXIX. Reciprocity Shaped Enclosures Calibration of Transducers Part XXVIII. Measurement of Part XXXI. Speech Acoustic Levels Intelligibility Part XXXII. Psychoacoustic Part XXX. Hearing Criteria A course in acoustics should be accompanied by a set of well-planned laboratory experiments. For example, the material of the first few chap­ ters will be more significant if accompanied by a laboratory experiment on noise measurement. This will familiarize the student with the meas­ urement of sound pressure and with the use of a frequency analyzer. He will appreciate more fully the meaning of sound pressure, sound intensity, decibels, sound energy density, and power level; and he will understand the accuracy with which noise can be measured. A suggested minimum of 10 experiments, listed both numerically for a year’s course and by term, is as follows: First Term Second Term No. 1. Noise measurement No. 3. Free-field calibration of microphones No. 2. Measurement of the con­ stants of an electro­ No. 5. Design and testing of a mechanical transducer loudspeaker baffle No. 8. Prediction and control of No. 4. Measurement of free-field noise in a ventilating response of a loudspeaker system No. 6. Study of sound fields in a No. 9. Audiometric testing of small rectangular hearing enclosure No. 10. Application of psycho­ No. 7. Study of sound fields in a acoustic criteria in the large irregular enclosure design of an auditorium An assignment of two problems per week should provide sufficient application of the material of the text. The short list of problems for each chapter should be supplemented by timely problems derived from the instructor’s experience. CONTENTS PREFACE........................................................................................................................ v SUGGESTIONS FOR INSTRUCTORS................................................................vii CHAPTER 1. INTRODUCTION AND TERMINOLOGY. . . . 1 part I Introduction........................................................................... 1 part II Terminology........................................................................... 8 CHAPTER 2. THE WAVE EQUATION AND SOLUTIONS . . . 16 part III The Wave Equation......................................................................16 part IV Solutions of the Wave Equation..................................................23 part V Energy Density and Intensity..................................................40 CHAPTER 3. ELECTRO-MECH^ NO-ACOUSTICAL CIRCUITS. . 47 part VI Mechanical Circuits......................................................................47 part VII Acoustical Circuits......................................................................62 part VIII Transducers...................................................................................70 part IX Circuit Theorems, Energy, and Power......................................77 CHAPTER 4. RADIATION OF SOUND..........................................................91 part X Directivity Patterns......................................................................91 part XI Directivity Index and Directivity Factor..............................109 CHAPTER 5. ACOUSTIC COMPONENTS.................................................116 part XII Radiation Impedances..............................................................116 part XIII Acoustic Elements....................................................................128 CHAPTER 6. MICROPHONES...........................................................................144 part XIV General Characteristics of Microphones....................................144 part XV Pressure Microphones..............................................................150 part XVI Gradient and Combination Microphones..............................178 CHAPTER 7. DIRECT-RADIATOR LOUDSPEAKERS . . . . 183 part XVII Basic Theory of Direct-radiator Loudspeakers 183 part XVIII Design Factors Affecting Direct-radiator Loudspeaker Performance..................................................................................195 be