Sound System Engineering

Sound System Engineering

Fourth Edition

Don DavisEugene Patronis, Jr.

Pat BrownEdited by

Glen Ballou

First published 1975by Howard W. Sams & Co., Inc.Indianapolis, Indiana 46268

This edition published 2013by Focal Press70 Blanchard Road, Suite 402, Burlington, MA 01803

Simultaneously published in the UKby Focal Press2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN

Focal Press is an imprint of the Taylor & Francis Group, an informa business

2013 Don Davis, Eugene Patronis, Jr. and Pat Brown

The right of Don Davis, Eugene Patronis, Jr. and Pat Brown to be identified as the authors of this work has been asserted by them in accordance with sections 77 and 78 of 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.

NoticesKnowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe.

Library of Congress Cataloging in Publication DataCIP data has been applied for

ISBN: 978-0-240-81846-7 (hbk)ISBN: 978-0-240-81847-4 (ebk)

Typeset in Times New Roman and Optimum by Glen Ballou

The fourth edition of Sound System Engineering is dedicated to

Carolyn Davis

who is the catalyst that made it happenand is the glue that held it all together.

ContentsPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xvChapter 1 Why Sound System Engineering? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Basic Electrical Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Hearing Versus Listening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Craftsmanship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Rigging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Literacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4The Art, Philosophy, and Science of Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

Chapter 2 Voices Out of the Past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7Significant Figures in the History of Audio and Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91893The Magic Year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11Bell Laboratories and Western Electric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11Harvey Fletcher (18841981) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12Harry Nyquist (18891976) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12The dB, dBm, and the VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12Sound System Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13Acoustic MeasurementsRichard C. Heyser (19311987) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13Calculators and Computers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14The Meaning of Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

Chapter 3 Sound and Our Brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17The Human Brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19The Current Era . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19Unexpected Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22

Chapter 4 Psychoacoustics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25Sound Reproduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25Is it Better to be Born Blind or Deaf ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26Recording Sound at the Eardrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27Psychoacoustics via a Metaphysical Foundation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27Barks, Bands, Equivalent Rectangular Bandwidths (ERBs), Phons and Sones . . . . . . . . . . . . . . . . . . . . .28

Chapter 5 Digital Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33Shannons Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35Dynamic Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36The Steps from Art to Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40Moravecs Warning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41Digital Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42What Is a Bit of Data? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43Bayesian Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47Planck System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47Bits, Nats, and Bans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48A Communication System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48Holography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49

Chapter 6 Mathematics for Audio Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51Engineering Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53Precision, Accuracy, and Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54Simple Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54vii

How to Add Gains and Losses Algebraically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54The Factor-Label System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55

viii ContentsBasic Physical Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58Mathematical Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60Complex Number Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64Decade Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65Converting Linear Scales to Logarithmic Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66Finding the Renard Series for Fractional Octave Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66Radians and Steradians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67Calculating Percentages and Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70Useful Math Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75A Little Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75The Origin of the Base of the Natural Logarithm, e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76The Complex Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77Eulers Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78Phasors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79Rates of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80

Chapter 7 Using the Decibel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .85The Decibel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87The Neper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87Concepts Underlying the Decibel and Its Use in Sound Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88Measuring Electrical Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90Levels in dB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91The Decibel in AcousticsLP, LW, and LI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92Acoustic Intensity Level (LI), Acoustic Power Level (LW), and Acoustic Pressure Level (LP) . . . . . . . . .93Inverse Square Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93Directivity Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .94Ohms Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .94A Decibel Is a Decibel Is a Decibel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95The Equivalent Level (LEQ) in Noise Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96Combining Decibels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97Combining Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99Using the Log Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99Finding the Logarithm of a Number to Any Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .100Semitone Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101System Gain Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101The VU and the VI Instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101Calculating the Number of Decades in a Frequency Span . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104Deflection of the Eardrum at Various Sound Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105The Phon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105The Tempered Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106Measuring Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106The Acoustical Meaning of Harmonic Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106Playback Systems in Studios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108Decibels and Percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110

Chapter 8 Interfacing Electrical and Acoustic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Alternating Current Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .115Electric Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117Properties of the LCR Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121Impedance Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126

Contents ixConstant Resistance Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .128Impedance Properties of Moving Coil Loudspeakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129Network Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132The Technicians Viewpoint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135Impedance Defined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135Handling the Acoustic Input and Output of the System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .137Total Electrical Gain of a System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142Interfacing the Electrical Output Power to the Acoustic Environment . . . . . . . . . . . . . . . . . . . . . . . . . . .143Gain Structure Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .150

Chapter 9 Loudspeaker Directivity and Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151Essential Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153Describing Q More Accurately . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .158Relationship Between C and Q in an Idealized Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159Idealized Loudspeaker Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160Class D Audio Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165Sound as a Weapon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166An Older View of Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .167

Chapter 10 The Acoustic Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169The Acoustic Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .171Dispersion and Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .171Inverse Square Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172Atmospheric Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172Velocity of Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .173Isothermal vs. Adiabatic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .173Temperature-Dependent Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .174The Effect of Altitude on the Velocity of Sound in Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175Typical Wavelengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175Doppler Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175Reflection and Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176Effect of a Space Heater on Flutter Echo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .177Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .177Definitions in Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178Classifying Sound Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178The Acoustic Environment Indoors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .186

Chapter 11 Audio and Acoustic Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .189Acoustic Analysis Sans Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .191Initial Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .191Acoustic Tests of Sound Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .192Examining AC Outlets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .193The ETC Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .195Site Surveys and Noise Criteria Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .203An Improper Use of Real Time Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .203Evaluation of Listener Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .205Fractional Bandwidth Filter Analyzers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .206Measuring Electromagnetic Pollution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .209Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .211

Chapter 12 Large Room Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .213What Is a Large Room? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .215Levels Defined: Sound Power Level (LW), Sound Intensity Level (LI), and Sound Pressure Level (LP) 220

x ContentsLevels in Enclosed Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .221Differentiating Between Reverberant Level and Reverberation Time . . . . . . . . . . . . . . . . . . . . . . . . . . .224Evaluation of Signal-to-Noise Ratio, SNR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .225Analyzing Reflections and Their Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .226Critical Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .228Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .233

Chapter 13 Small Room Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .235Non-Statistical Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .237Small Room Acoustical Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .238Small Room Reverberation Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .238Small Room Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .239Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .239What Is an Eigen Mode? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .239Small Room Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .240The Initial Signal Delay Gap (ISD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .240Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .242Reflection Free Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .244Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .245Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .248

Chapter 14 Designing for Acoustic Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .251Maximum Physical Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .253Establishing an Acceptable Signal-to-Noise Ratio (SNR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .253Establishing an EAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .254Needed Acoustic Gain (NAG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .254The Number of Open Microphones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .255The Feedback Stability Margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .255Calculating Potential Acoustic Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .256Obtaining Dx Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .258Measuring Acoustic Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .259Achieving Potential Acoustic Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .259Limiting Parameters in Sound Reinforcement System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .260How Much Electrical Power Is Required? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .260Finding the Required Electrical Power (REP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .261Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .263

Chapter 15 Designing for Speech Intelligibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .265Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .267Articulation Losses of Consonants in Speech . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .268Maxfields Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .270Speech Power and Articulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .270Signal-to-Noise Ratio (SNR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .271Speech Intelligibility Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .271Non-Acoustic Articulation Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .275Relationship Between QMIN and D2(MAX) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .276High Density Overhead Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .276%ALCONS Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .277A Little HistoryIntelligibility Workshop 1986 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .278Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .279

Chapter 16 What is Waving and Why . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .281General Properties of Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .283Plane Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .288Non-Planar Wave Motion in a Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .297Plane Wave Tubes having Arbitrary Terminations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .299

Contents xiImpedance Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .303More General Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .305Acoustic Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .308Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .309Acoustic Dipole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .310

Chapter 17 Microphones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313The Microphone as the System Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .315Microphone Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .315Thermal Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .317Microphone Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .324Nature of Response and Directional Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .325Boundary Microphones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .330Wireless Microphones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .335Microphone Connectors, Cables, and Phantom Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .339Measurement Microphones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .341Microphone Calibrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .342

Chapter 18 Loudspeakers and Loudspeaker Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .345Loudspeaker Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .347Radiated Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .358Axial Sound Pressure Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .363Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .363Loudspeaker Electrical Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .364Loudspeaker Directivity Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .365Loudspeaker Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .365Direct Radiator Example Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .366Horns and Compression Drivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .368Practical Considerations Involving Horns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .374Horn Compression Drivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .376Crossover Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .378Loudspeaker Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .392Bessel Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .398Line Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .400Vented Enclosure Bass Loudspeakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .412Large Signal Behavior of Loudspeakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .420

Chapter 19 Power Ratings for Amplifiers and Loudspeakers . . . . . . . . . . . . . . . . . . . . . . . . .423Loudspeaker Power Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .425Active Loudspeaker Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .428Non-Linear Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .428The Amplifier as a Voltage Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .429The Equivalent Amplifier SizeEAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .430Power from a Voltage Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .431Burst Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .433Power Rating Possibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .434Putting It All Together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .435Multi-way Loudspeakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .438System Gain Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .439Combining MIV and EAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .439

Chapter 20 Computer-Aided System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .441Spherical Loudspeaker Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .443Near Field vs. Far Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .444The Measurement Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .445Loudspeaker Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .447

xii ContentsDirect Field Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .449Room Model Detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .449Room AcousticsAn Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .451Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .453Realistic Room Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .457Universal Room Modeling Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .460Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .461

Chapter 21 Signal Delay and Signal Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .463Signal Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .465Useful Signal Delay Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .466Synchronization and Alignment of Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .469Finding Acoustic Origins of Unlike Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .470Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .472

Chapter 22 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .475Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .477Analog to Digital Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .497System Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .502Digital Systems and the Z Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .520Dynamics Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .528

Chapter 23 Digital Audio Formats and Transports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .533The Analog Waveform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .535Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .535Digital Signal ProcessingDSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .542Two Data Camps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .543How Does Ethernet Work? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .545Ethernet Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .546An Open Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .549AES3 vs. AoE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .549Hybrid and Proprietary Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .549Analog vs. Digital Audio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .550

Chapter 24 Sound System Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .553System Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .555Early Research on Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .555The Transient Nature of Acoustic Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .556Introduction of Real-Time Analyzers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .559Band-Rejection, Bandpass, and Band-Boost Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .562TEF Analysis in Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .567How to Approach Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .568What Can an Equalizer Equalize? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .570A Real-Time Regenerative-Response Method of Equalizing a Sound System . . . . . . . . . . . . . . . . . . . . .572Equalizing for Playback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .573An Improper Use of Real Time Analysis in Monitoring Music and Speech . . . . . . . . . . . . . . . . . . . . . . .574Diaphragmatic Absorbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .574Dont Equalize for Hearing Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .575Proximity Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .575Checking Microphone Polarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .575Loudspeaker Polarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .576Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .576

Chapter 25 Putting It All Together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .577Acoustical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .579Alternative Solutions for a Given Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .579Device Interconnections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .582

Analog Interconnection Circuitry Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .583Signal CablesAnalog Audio, Digital Audio, and Video . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .590AES3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .597Computer Control and Communication of Digital Audio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .602

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .605Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .609

PrefaceThere are two worlds in audioone of wave equations, Fourier, Hilbert, and Laplace transforms, and the otherof Ohms Law, Sabine and Hopkins Stryker. Eugene Patronis, Jr., straddles both like a colossus, as he is able totheorize in Quantum Mechanics and design, build, and service, with his own hands, all components used inaudio.

Pat Brown is our new co-author and brings to this volume unique tools he has developed in the course ofhis loudspeaker testing, particularly directivity measurements, into the twenty-first century. He has taughtSyn-Aud-Con seminars all over the world in person as well as through his internet training programs. He is alongtime friend of both Dr. Patronis and Don Davis, and like them, a man who delights in fully sharing hisknowledge of sound system engineering with others. We welcome his participation in this volume.

The authors come from two quite different backgrounds: one is academic, the others are industrial and fieldoriented. The lion is known by his claw was said of Newton, whereas the technician approach uses a broadbrush to get a workable, if not elegant, answer. Therefore, we have identified each authors contribution sepa-rately. Its your privilege to select the approach most applicable to your need. With todays generation of com-puter users and the wealth of available software its you, the reader, who chooses the boundaries of yourinterests and academic skills. It is our wish that whatever background you bring to the subject you will findnew tools for that level and hints of the next.

Sound System Engineering is a widely sold, widely used text on sound system design. The first editionswere oriented toward those planning systems from components available in the existing marketplace, i.e., theywere treated as boxes on a diagram. The first editions ignored component design and analysis other than theirinterconnecting parameters.

When Don and Carolyn Davis, the authors of the first two editions, sought specific advice on componentdesign and in-depth analysis of given components they turned to their long time friend and mentor, EugenePatronis, Jr. to provide the in-depth analysis he excels in. You will find in this edition both approaches, allow-ing newcomers to operate efficiently while providing the more experienced an opportunity to achieve a moreadvanced viewpoint. We know that one can start reading on one level, but as our experience and expertisedevelops, we are grateful for the more advanced approach. What we read as our learning process starts is muchdifferent years later and we become very grateful for the more advanced material.

Those who have benefited from a rigorous and thorough academic background will find that EugenePatronis work is a succinct summary of all you should have absorbed intellectually whereas the less sophisti-cated approach may contain useful nuggets that have surmounted gray areas in system compromises. Thisdual approach provides some seemingly uneven interconnects but benefits from the diverse experience of theauthors.

The authors have retained their own mental images of who they are writing for, often a combination of bothapproaches. We hope that you will find this volume useful in pursuit of our mutual goal of truly engineeredrather than merely assembled sound systems.

Thanks to Glen Ballou

Our special thanks to Glen Ballou, who transcribed our material into a publishable format. These simple wordscant begin to describe the agony he has endured.

Pat Brown,

Don Davis,viiEugene Patronis, Jr.

Chapter 1Why Sound System Engineering?

by Don Davis1.1 Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Basic Electrical Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Hearing Versus Listening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.5 Craftsmanship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.6 Rigging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.7 Literacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.8 The Art, Philosophy, and Science of Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.9 Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Why Sound System Engineering? 3Sound has over the centuries been associated withhuman hearing (i.e.: Is there a sound if a tree fallsin the forest without a listener present?) Accordingto Webster, The sensation perceived by the sense ofhearing. Also from Webster: Audio, on the otherhand, has largely been associated with electricalcommunication circuits.

System is a word we use to describe anyexperience cluster that we can map as a set ofinteracting elements over time. Typically a system ismapped by identifying the pathways of informationflow, as well as possibly the flow of energy, matter,and other variables. But the flow of information isspecial; because only information can go from A toB while also staying at A. (Consider: photocopymachines would be useless if one didnt get to keepthe original). Digital systems, analog systems,acoustic systems, etc. should be regarded by asystem engineer as so many black boxes that needto be matched, interconnected, and adjusted. Theinternal circuitry should be the interest of thecomponent designer/manufacturer.

1.1 Prerequisites

What kind of background should an aspiring soundsystem engineer possess is an often asked question.A list of desirable experiences would include:

1. Some basic electrical training.2. An interest in mathematics.3. A good ear (a love of quality sound and acute

aural senses).4. Skill with basic tools.5. Some appreciation of the perils of rigging.6. Good reading and writing skills.7. A genuine appreciation for the art, philosophy,

and science of sound.

1.2 Basic Electrical Training

Time spent as an apprentice electrician is notwasted. In many cases, large sound systems dealwith separate power systems, and safety springsfrom knowledge of the power circuits that areinvolved. Conduits, cable sizes, and types ofgrounding and shielding can be complex even atpower frequencies. Knowledge of the electricalcodes is a necessary fundamental tool.

1.3 Mathematics

From Ohms law to the bidding process, an abilityto quickly learn new algorithms both speeds upprocesses and ensure profits. In todays markets cutand try is too expensive of both time and money toallow avoidance of basic computer skills; the use ofprograms such as Mathcad for both technical andfinancial calculations is important. Knowing whatthe formulae actually used are doing is essential. Inorder to trust any computer program, having done itfirst on paper the hard way, provides knowledge andconfidence in the fast way and leaves you capable ofdetecting unexpected anomalies that might occur.Yes! You do need more than arithmetic.

1.4 Hearing Versus Listening

We all hear. But what we listen to depends to a largedegree on our previous listening experiences. I haveoften stood in the center of an acoustic anomalysuch as a reflection from an undesirable angle,distance, and level, that was destroying speech intel-ligibility, and watched the startled expression on theface of a person sitting in the pew as a piece ofacoustical material is passed between his ears andthe reflection, which restored intelligibility.

Once experienced, your eyes, ears, and brain, canrecognize such problems by simply walking throughthem. Sensitive listening is a great plus in soundsystem work, and it is a sufficient reason to hear asmany venues as possible under normal usage condi-tions. I am always surprised when I see engineerstrying to design a church sound system from a set ofdrawings without ever having attended a service tosee what their actual needs are versus what theydlike to provide them.

Because all sound system design starts in theacoustic environment and works back from there tothe input, failure to experience the normal use of thespace can be fatal to the ultimate end result. On oneoccasion I was listening in a mammoth cathedralfrom a position behind the altar, when asked by theadministrator, if our design could solve their intelli-gibility problem. The priest about to conduct theservice spoke to me, and because of a combinationof a speech defect and in a foreign accent, I wasunable to understand him to sufficiently compre-hend his message. I had to tell the administrator thatour system could only raise the priests audio level,not his intelligibility.

Watching successful ministers, politicians, andother public figures use microphones reveals aworld of problems unaddressed by the most compe-

4 Chapter 1tent engineer. In one case the engineer was asked ifhe could put more soul in the monitor.

1.5 Craftsmanship

Possession of a guitar does not make one a musiciannor do tools make a craftsman. Skill with basic toolsmanifests itself in clean solder joints, orderlycabling, careful labeling on panels and terminals.Construction of successful loudspeaker arrays is achallenge to both artistry and craftsmanship. In myexperience craftsmanship is a direct expression ofcharacter.

1.6 Rigging

Rigging, in itself, is a business as complex and diffi-cult as engineering the sound system and oftenbehooves sound contractors to seek out professionalassistance when required to hang large, heavy, andexpensive loudspeaker arrays.

I was involved in a consulting job for a majorpublic arena venue where the owner intended tohang the new array from the previous arraysrigging. (A complicated system of cables and drumsfor raising and lowering the arrays). I insisted ontheir hiring a notable rigging authority who went upinto the rigging with a camera and came down witha dozen photographs of impending disasters, such asgrooves worn in the drums by the cables, frayedcables, unsafe connectors, and a lack of safetycables, to cite but a few of the problems. There arerecorded fatalities from falling arrays. It is not abusiness for amateurs.

1.7 Literacy

This would seem obvious, but is often a weak link inan otherwise successful background experience.Sales presentations, bid offers, instruction manualsfor the operators of your systems, all require readingand writing skills. Communications with customers,suppliers, and consultants needs to be thoughtfullyand concisely written. For example, the contractorshould be on record telling the customer that thedesign will function properly only if the HVACcontractor meets the specified noise criteria that isprovided in the Specification. Failure to do so can bedisastrous. A memo on file with the owner can savethe sound contractor and/or consultant from havingto take the blame.

1.8 The Art, Philosophy, and Science of Sound

The design of well-engineered sound systems standson the shoulders of the giants who created thecommunication industry. Art precedes science isan axiom that is eternally true. Prof. Higgins asportrayed in the film, My Fair Lady, exemplifiedthe majesty of language, the science of studying itsproper sounds, and meanings, and the engineeringsystems used in that earlier day. Even today the mostdifficult sound systems to design, build, and operateare those used in the reinforcement of live speech.Systems that are notoriously poor at speech rein-forcement often pass reinforcing music with flyingcolors. Mega churches find that the music reproduc-tion and reinforcement systems are often best sepa-rated into two systems

1.9 Fields

From my first view of the rainbow depiction of theelectromagnetic spectrum from dc to gamma ray Ihave striven to gain a conceptual mental view ofvarious fields, Fig. 1-1. Physical science, during thepast century, has come to the conclusion that theUniverse is some sort of field. The nature of thisuniversal field remains controversialis it matterwhich has mass? Or something more ethereal suchas information?

Michael Faraday, 1831, said Perhaps someforce is emanating from the wire.

A Cambridge man said Faraday, let me assureyou, at Cambridge our electricity flows through thewire.

Oliver Heaviside, 1882, from his book, ElectricalPapers, Vol. 1:

Had we not better give up the ideathat energy is transmitted through thewire altogether? That is the plaincourse. The energy from the batteryneither goes through the wire one waynor the other. Nor is it standing still, thetransmission takes place ent irelythrough the dielectric. What, then, is thewire? It is the sink into which the energyis poured from the dielectric and therewasted, passing from the electricalsystem altogether.

John Ambrose Fleming in 1898 wrote:

It is important that the student shouldbear in mind that, although we areaccustomed to speak of current asflowing through the wire in one direc-tion or the other, this is a mere form of

Why Sound System Engineering? 5words. What we call the current in thewire is, to a large extent, a processgoing on in the space or materialoutside the wire.

Ernst Guillmin, Communications Networks, Vol.II, 1935

Heavis ide is the only one whoconsiders the nature of the sources aswell as the boundary effects both for theinitial buildup or transient behavior andfor the steady-state condition. He is thefirst also, to consider the leakagethrough the insulation, in view of whichthe true significance of the inductanceparameter may be appreciated. Hiswork is a first approximation only ascompared with other, more rigoroustreatments. For the engineer, however,this first approximation is usually suffi-cient.

Further,

The concept of guided waves, beforeMaxwell, the physical picture of thepropagation of electricity through along circuit was more or less that whichis frequently presented in elementarytextbooks, where the hydraulic analogyto an electr ic c ircui t is given forpurposes of visualization. That is, theseat of the phenomenon was taken to bewithin the conductor. What occurredoutside the conductor could be neitherdefinitely formulated nor described. Theelectrical energy was thought of asbeing transmitted through the conductorwhich, therefore, became of primeimportance. In fact, if we accept thispoint of view altogether, it becomesimpossible to conceive of a flow of elec-trical energy from one point to anotherwithout the aid of an interveningconductor of some sort. It has been thewriters experience that many studentsare quite wedded to this point of view, somuch so, in fact, that to them the propa-gation of energy without wires (wirelesstransmission) becomes a thing alto-gether apart from other forms of trans-miss ion involving an in terveningconducting medium.

An appreciation of Maxwells theory of electro-magnetic wave propagation brings the so-calledwireless and wired forms of transmission under the

same roof, so to speak. They merely appear asspecial cases of the same fundamental phenom-enon. The presence of a conductor merely causesthe field be broken up into various components,some of which are assigned to the conductor itself,others to the surrounding medium, and still others tothe surface separating the two media.

From the Standard Handbook for ElectricalEngineers by Donald G. Fink and H. WayneBeaty. There is a section entitled, Electromag-netic Wave Propagation Phenomenon.

The usually accepted view that the conductorcurrent produces a magnetic field surrounding itmust be displaced by the more appropriate one thatthe electromagnetic field surrounding the conductorproduces, through a small drain on the energysupply, the current in the conductor. Although thevalue of the latter may be used in computing trans-mitted energy, one should clearly recognize thatphysically this current produces only a loss and inno way has a direct part in the phenomenon ofpower transmission.

Ralph Morrisons website has some commentson electromagnetic laws.

The laws I want to talk about are the basic lawsof electricity. Im not referring to circuit theory lawsas described by Kirchhoff or Ohm but the lawsgoverning the electric and magnetic fields. Thesefields are fundamental to all electrical activitywhether the phenomenon is lightning, electrostaticdisplay, radar, antennas, sunlight, and power gener-ation, analog or digital circuitry. These laws areoften called Maxwells equations. Light energy canbe directed by lenses, radar energy can be directedby waveguides and the energy and power frequen-cies can be directed by copper conductors. Thus wedirect energy flow at different frequencies by usingdifferent materials. For utility power the energytravels in the space between conductors not in theconductors. In digital circuits the signals and energytravel in the spaces between traces or between thetraces and the conducting surfaces. Buildings havehalls and walls. People move in the halls not thewalls. Circuits have traces and spaces, signals andenergy moves in the spaces not in the traces.

Scanning the Electromagnetic Spectrum Chartfrom dc through radio waves, light itself, out togamma rays we can see that electromagnetic fieldsplay a key part in our lives, Fig. 1-1.

Researchers studying human consciousness arefinding electromagnetic phenomenon in addition tothe previously known electrical phenomena. WhenEMI (electromagnetic interference) occurs in audiosystems RF spectrum analyzers can be useful tools.

6 Chapter 1Figure 1-1. Electromagnetic spectrum chart.

Chapter 2Voices Out of the Past

by Don Davis2.1 Significant Figures in the History of Audio and Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 1893The Magic Year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Bell laboratories and Western Electric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Harvey Fletcher (18841981) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.5 Harry Nyquist (18891976) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.6 The dB, dBm, and the VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.7 Sound System Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.8 Acoustic MeasurementsRichard C. Heyser (19311987) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.9 Calculators and Computers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.10 The Meaning of Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.11 Historical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Voices Out of the Past 9During the fall of 1978, we stopped in Williams-burg, Virginia. As is our habit, we explored theold-bookstores and asked whether they had anybooks on acoustics. We were told they had just one,an old one. They brought out a vellum bound firstedition dated 1657, Magiae Universalis by GaspareP. Schotto (16081666).

He was a colleague of Athanasius Kircher(16021680) whose work was discussed in Fred-erick Vinton Hunts valuable book Origins inAcoustics. The book, written in Latin, was publishedat Herbipoli, the modern Wurzburg, Germany. Someof the plates from it are shown in Figs. 2-1 through2-6.

In researching the history of this book we foundthat it was mentioned in the Edinburgh magazine(volume 12, page 322) in 1790, as well as in Hunts,Origins in Acoustics, regarding Boyle and Hookeswork. Magiae Universalis was used by RobertBoyle (16271691) and his assistant Robert Hooke(16351703) as they worked to improve air pumpsand experiment with ticking watches in vacuums.

This book described Otto Von Guerickes workwith air pumps.

An erudite discussion of Athanasius Kirchersbook, Phonurgia Nova by Lamberto Tronchin inJanuary 2009 edition of Acoustics Today, providesone of the best surveys of the period under discus-

sion. Richard C. Heyser put it best when he said,You dont really own that book, you are its tempo-rary custodian.

These men were Galileos contemporaries andwere representative of the desire for scientificknowledge, as well as the collectors of all the mythsof their age.

2.1 Significant Figures in the History of Audio and Acoustics*

Often, in the modern scheme of things, history is notmandatory in engineering classes taught at theuniversity level. Significant historical figures areencountered as Faradays ice-pail experiment,Maxwells equations, Ohms law etc., but notstudied in depth.

Electrical engineers encounter the SI terms, poten-tial difference in volts (Alessandro Volta), current inamperes (Andre Marie Ampere), capacitance infarads (Michael Faraday), and thermodynamictemperature in Kelvin (Lord Kelvin), as units ofmeasurement. These were living breathing men whohad occasion to interact with each other and inter-mingle their ideas to the benefit of science. Greatseminal ideas belong to the individual, but the inter-

Figure 2-1. Frontpiece of a book published in 1857 atHerbipoli, the modern Wurzburg, Germany.

Figure 2-2. Water-powered musical instrument thatfascinated our forefathers as much as computersinterest us today. From Magiae Universalis.

*. Significant Figures in the History of Audioand Acoustics is an edited version of thechapter, Audio & Acoustic DNADo youKnow Your Audio and Acoustic Ancestors? inthe 4th Edition of the Handbook for Sound Engi-neers, edited by Glen Ballou.

10 Chapter 2mingling of them leads industries. Their predeces-sors and contemporaries such as Joule (work, energy,heat), Charles Coulomb (electric charge), Isaac

Newton (force), Hertz (frequency), Watt (power,radiant flux), Weber (magnetic flux), Tesla (magneticflux density), Henry (inductance), and Siemens

Figure 2-3. The first bugging system. Horns such asthese were used by Athanasius Kircher, a contempo-rary of Kasper Schott, to speak to the gatekeeper fromhis quarters and to eavesdrop on the conversationtaking place in the courtyard. His experimental hornwas 22 palms long. (A palm is about 8.7 inches, so hishorn was about 16 feet long). From Magiae Universalis.

Figure 2-4. The basic rules for sound reflection as ageometric problem. From Magiae Universalis.

Figure 2-5. How oracles talk or music can be trans-mitted from one space to another. From Magiae Univer-salis.

Figure 2-6. Illustrations of reflections, focusing, diffu-sion, time delay, and creeping. From Magiae Univer-salis.

Voices Out of the Past 11(conductance), are immortalized as international SIderived units. Kelvin and Ampere alone have namesinscribed as SI base units. Kirchhoff diagrams definethe use of these units in circuit theory.

What the study of these mens lives provides, tothe genuinely interested reader, is the often uniqueway the great ideas came to these men, the persistentpursuit of the first glimmer, and the serendipity thatcomes from sharing ideas with other talented minds.As all of this worked its way into the organizedthinking of mankind, one of the most importantinnovations was the development of technical soci-eties formed around the time of Newton, whereideas could be heard by a large receptive audience.

Some of the worlds best mathematicians strug-gled to quantify sound in air, in enclosures and in allmanner of confining pathways. Since the time ofEuler (17071783), Lagrange (17361813), anddAlembert (17171783), mathematical tools existedto analyze wave motion and develop field theory.

By the birth of the twentieth century, workers inthe telephone industry comprised the most talentedmathematicians and experimenters in both what wasto become electronics and in acoustics. At MIT, thereplacement of Oliver Heavisides operationalcalculus by Laplace transforms gave them an envi-able technical lead in education.

2.2 1893The Magic Year

At the April 18, 1893 meeting of the American Insti-tute of Electrical Engineers in New York City,Arthur Edwin Kennelly (18611939) gave a paperentitled Impedance.

That same year General Electric, at the insistenceof Edwin W. Rice, purchased Rudolph Eicke-meyers company for his transformer patents. Thegenius, Charles Proteus Steinmetz (18651923),worked for Eickemeyer. In the saga of great ideas, Ihave always been as intrigued by the managers ofgreat men, as much as the great men themselves. E.W. Rice of General Electric personified true leader-ship when he looked past the misshaped dwarf thatwas Steinmetz, to the mind present in the man.General Electrics engineering preeminence, inthose years, proceeded directly from Rices extraor-dinary hiring of Steinmetz.

Dr. Michael I. Pupin of Columbia University waspresent at the Kennelly paper. Pupin mentionedOliver Heavisides use of the word impedance in1887. This meeting established the correct definitionof the word and established its use within the elec-tric industry. Kennellys paper, along with thegroundwork laid by Oliver Heaviside in 1887, was

instrumental in introducing the terms being estab-lished in the minds of Kennellys peers.

The truly extraordinary Arthur Edwin Kennelly,(18611939) left school at the age of thirteen andtaught himself physics while working as a telegra-pher. He is said to have planned and used his timewith great efficiency, which is evidenced by hisbecoming a member of the faculty of Harvard in1902 while also holding a joint appointment at MITfrom 19131924. He was the author of ten booksand the co-author of eighteen more, as well aswriting more than 350 technical papers. Edison hademployed A. E. Kennelly to provide physics andmathematics to Edisons intuition and cut and tryexperimentation. The reflecting ionosphere theory isjointly credited to Kennelly and Heaviside, andknown as the Kennelly-Heaviside layer. One ofKennellys PhD students was Vannevar Bush, whoran Americas WWII scientific endeavors.

Steinmetz was not at the April 18, 1893 meeting,but sent in a letter-of-comment which included:

It is however, the first instance here,so far as I know, that the attention isdrawn by Mr. Kennelly to the corre-spondence between the electrical termimpedance and the complex numbers.The importance hereof l ies in thefollowing: the analysis of the complexplane is very well worked out, hence byreducing the technical problems to theanalysis of complex quantities they arebrought within the scope of a known andwell understood science.

Nikola Tesla (18561943) working with West-inghouse designed the ac generator that was chosenin 1893 to power the Chicago Worlds Fair.

2.3 Bell laboratories and Western Electric

The University of Chicago, at the end of the Nine-teenth Century and the beginning of the TwentiethCentury, had Robert Millikan, Americas foremostphysicist. Frank Jewett, who had a doctorate inphysics from MIT, and now worked for WesternElectric, was able to recruit Millikans top students.George A. Campbell (18701954) had by 1899 devel-oped successful loading coils capable of extendingthe range and quality of the, at that time, unamplifiedtelephone circuits. Unfortunately, Prof. MichaelPupin had also conceived the idea and beat him to thepatent office. Bell telephone paid Pupin $435,000 forthe patent and by 1925, the Campbell designedloading coils had saved Bell Telephone Company$100,000,000 in the cost of copper wire alone.

12 Chapter 2To sense the ability of loading coils to extend therange of unamplified telephone circuits, Bell hadreached New York to Denver by their means alone.Until Thomas B. Doolittle evolved a method in 1877for the manufacture of hard drawn copper, the metalhad been unusable for telephony due to its inabilityto support its own weight over usable distances.Copper wire went from a tensile strength of 28,000pounds per square inch with an elongation of 37%,to a tensile strength of 65,000 pounds per squareinch and a elongation of 1%.

H. D. Arnold, with the advent of usable copperwire, the vacuum tube amplifier, 130,000 telephonepoles, and 25 tons of copper wire was able to estab-lish transcontinental telephony in the year 1915.There was also a public address system at thoseceremonies celebrating this accomplishment.

2.4 Harvey Fletcher (18841981)

In 1933, Harvey Fletcher, Steinberg and Snow,Wente and Thuras and a host of other Bell Labsengineers gave birth to Audio Perspective demon-strations of three channel stereophonic soundcapable of exceeding the dynamic range of the liveorchestra. Their exhaustive study led to the conclu-sion that to reproduce the sound field would requirean infinite number of sources and that the bestcompromise lay in three channels. They alsodemonstrated that two channels were sufficient overheadphones for binaural recordings. They under-stood that for stereophonic reproduction each of thethree channels had to cover all of the audience, afact many contemporaries are unaware of. Early inmy career at Altec, I had the privilege of workingwith William Snow and having full discussions oftheir 1933 system.

Edward C. Wente and Albert L.Thuras wereresponsible for the full range, low distortion,high-powered sound reproduction using condensermicrophones, compression drivers, multicellularexponential horns, and horn loaded low-frequencyenclosures, all of which were their original designs.The Fletcher loudspeaker, as designed by Wente andThuras, was a three-way unit consisting of an 18inch low-frequency driver horn loaded woofer, theincomparable W. E. 555 as a mid range, and theW. E. 597A high-frequency unit.

The power amplifiers and transmission lineswere capable of full dynamic range from 30 Hz to15,000 Hz, capabilities often claimed today butseldom realized.

In 1959, Carolyn and I repeated the originalgeometry tests of the 1933 experiments whileworking for Klipsch and Associates. Mr Klipsch and

I then traveled to Bell Telephone Laboratories inNew Jersey, where we made a demonstration of ourresults using Klipsch horns in the Arnold Audito-rium. After our demonstration we were shown oneof the original Fletcher loudspeakers.

A perspective can be gained, compared totodays products, when it is realized that WesternElectric components like the 555 and the 597 are tobe found today in Japan, where originals sell for upto five figures. It is estimated that 99% of theexisting units are in Japan. It is of interest to notethat many of todays seekers of quality sound repro-duction are still building tube-type amplifiersemploying the W. E. 300 B vacuum tubes.

2.5 Harry Nyquist (18891976)

The word inspired means to have been touched bythe hand of God. Harry Nyquists thirty-sevenyears and 138 US patents while at Bell TelephoneLaboratories personifies inspired. In acoustics theNyquist plot is, by far, my favorite for a first look atan environment driven by unknown source. Nyquistalso worked out the mathematics that allowedamplifier stability to be calculated leaving us theNyquist plot which is one of the most useful audioand acoustic analysis tools ever developed. Hiscohort, Hendrik Bodie, gave us the frequency andphase plots as separate measurements.

Karl Kupfmuller (18971977) was a Germanengineer who paralleled Nyquist work, indepen-dently deriving fundamental results in informationtransmission, in closed loop modeling, including astability criterion. Kupfmuller as early as 1928 usedblock diagrams to represent closed loop linearcircuits. He is believed to be the first to do so.

Todays computers, as well as digital audiodevices, were first envisioned in the mid-1800s byCharles Babbage. The mathematics discussed byLady Lovelace, the only legitimate daughter of LordByron, even predicted the use of a computer togenerate musical tones.

Claude Shannon went from Nyquists paper onthe mathematical limit of communication to developInformation Theory, which is so important totodays communication channels.

2.6 The dB, dBm, and the VI

The development of the dB from the mile of stan-dard cable by Bell Labs, their development andsharing of the decibel, the dBm, and the VU via the

Voices Out of the Past 13design of VI devices, changed system design into anengineering design.

The first motion pictures were silent. Fortuneswere made by actors who could convey visualemotion. When motion pictures acquired sound in1928, again via Western Electrics efforts, a largenumber of these well-known personalities failed tomake the transition from silent to sound. The facesand figures failed to match the voices the minds ofthe silent movie viewers had assigned them. Later,when radio became television almost all the radiotalent was able to make the transition because thefamiliar voices predominated over any mental visualimage the radio listener had assigned to thatperformer. Often, at the opera, the great voices willnot look the part, but just a few notes nullify anynegative visual impression for the true lover ofopera, whereas appearance will not compensate fora really bad voice.

In 1928, a group of Western Electric engineersbecame the Electrical Research Products, Inc.(ERPI), in order to service the motion picturetheaters using Western Electric sound equipment. Atthe termination of World War II, the standard for thebest bass reproduction was the loudspeakersinstalled in the better motion picture theaters. Thegoal of the designers of consumer component audioreproduction was to approach the motion picturetheater quality. Western Electric had decimated theircompetition, RCA, in the theater business, so RCAwent to court and obtained a consent decree whichrestricted Western Electric in the field of motionpicture sound. At this point some of the engineersinvolved formed All Technical Services (Altec),which is why it is pronounced all tech, not al-tect.One of the pioneer engineers told me, Those dayswere the equivalent of one ohm across Fort Knox.They bought the Western Electric theater inventoryfor pennies on the dollar.They also bought theLansing Manufacturing Company and PeerlessManufacturing which brought James B. Lansing,Ercel Harrison and Bill Martin (Jim Lansingsbrother) into Altec.

2.7 Sound System Equalization

Dr. Wayne Rudmose was the earliest researcher toperform meaningful sound system equalization.Dr. Rudmose published a truly remarkable paper inNoise Control (a supplementary Journal of theAcoustical Society of America) in July 1958. At theAES session in the fall of 1967, I gave the firstpaper on the one-third of an octave contiguousequalizer, which Altec named Acousta-Voicing.Dr. Rudmose was chairman of that AES session.

The control these equalizers allowed over acousticfeedback in live sound systems quickly led to muchmore powerful sound reinforcement systems.

I introduced variable system equalization inspecial sessions at the screening facilities in August1969 to the head sound men, Fred Wilson at MGM,Herb Taylor at Disney, and Al Green at Warner Bros.Seven Arts. These demonstrations were prior to myleaving Altec to start Synergetic Audio Concepts andothers reaped the benefits of this work.

Some early workers in equalization imaginedthey were equalizing the room; equalization is elec-trical, not acoustical, and what it always adjusts isthe input to the loudspeaker terminals. It allowedfeedback in a reinforcement system, containing ahighly efficient, but uneven amplitude responseloudspeaker, to be controlled, while increasing theacoustic energy in the room.

2.8 Acoustic MeasurementsRichard C. Heyser (19311987)

Plato said, God ever geometrizes. Richard Heyser,the geometer, should feel at ease with God. To thosewhose minds respond to the visual, Heyser smeasurements shed a bright light on difficult mathe-matical concepts. Working from Dennis Gabors(19001979) analytic signal theory, the Heyser spiraldisplays the concept of the complex plane in a singlevisual flash. Heyser was a scientist in the purestsense of the word, employed by NASA, and audiowas his hobby. When I first met Richard C Heyser inthe mid-1960s, Richard worked for Jet PropulsionLaboratory as a senior scientist. He invited me to hishome to see his personal laboratory. The first thinghe showed me on his Time Delay Spectrometry(TDS) equipment was the Nyquist plot of a crossovernetwork he was examining.

I gave the display a quick look and said, Thatlooks like a Nyquist plot!

He replied, It is.But, I said, no one makes a Nyquist analyzer.Thats right, he replied.At this point I entered the modern age of audio

analysis. It was a revelation to watch Dick tuning inthe signal delay between his microphone and theloudspeaker he was testing until the correct band-pass filter Nyquist display appeared on the screen.Seeing the epicycles caused by resonances in theloudspeaker, and the passage of non-minimumphase responses back through all quadrants, openedup a million questions.

Heysers work led to loudspeakers with vastlyimproved spatial response, something totally unrec-ognized in the amplitude-only days. Arrays became

14 Chapter 2predictable and coherent. Signal alignment enteredthe thought of system designers. Heysers EnvelopeTime Curve (ETC) technology resulted in thechance to meaningfully study loudspeakerroominteractions.

Because the most widely taught mathematicaltools proceed from impulse responses, Heyserstransform is perceived through a glass darkly. It isleft in the hands of practitioners to further researchinto the transient behavior of loudspeakers. Thedecades-long lag of academia will eventually applythe lessons of the Heyser transform to transducersignal delay and signal delay interactions.

I hold Harry Olson of RCA in high regardbecause, as the editor of the Journal of the AudioEngineering Society in 1969, he found Richard C.Heysers original paper in the wastebasket; it hadbeen rejected by means of that societys inadequate,at that time, peer review system.

2.9 Calculators and Computers

Richard C. Heyser gave us the instrumentation andTom Osborne of Hewlett-Packard gave us the mathe-matical tools to begin to understand what we wereactually doing in both electronics and acoustics asapplied to sound reinforcement systems. Back in the1960s , we u t i l i z ed t e s t equ ipmen t f romHewlett-Packard, General Radio,Tektronics, andBruel and Kjaer. I purchased one of the very firstHewlett-Packard 9100 computer calculatorsdesigned by Tom Osborne. The 9100s transcen-dental functions, memory, and print out facilities ledto lengthy acoustic design algorithms. Many of thesesame algorithms are still used in todays computers.

When the HP 35 handheld calculator, so namedfor its thirty-fiv