HANDBOOK FOR SOUND ENGINEERS THE NEW AUDIO CYCLOPEDIA

AUDIO LIBRARY

Audio IC Op-Amp Applications, 3rd Edition Walter G. Jung

Audio Production Techniques for Video David Miles Huber Handbook for Sound Engineers: The Ne\\i Audio Cyclopedia Glen Ballou, Editor Ho\v to Build Speaker Enclosures Alexis Badmaieff and Don Dan's

Introduction to Professional Recording Techniques Bruce Bartlett (John Woram Audio Series)

John D. Lenk's Troubleshooting & Repair of Audio Equipnlent John D. Lenk

Modern Recording 'I'echniques, 2nd Edition Robert E. Runstein and David Miles Huber Musical Applications of l\iicroprocessors, 2nd Edition llal Chambe rUn

Principles of Digital Audio Ken C. Pohlmann

Random Access Audio David Miles lluber Recording Studio Technology John Woram Sound System Engineering, 2nd Edition Don and Carolyn Davis

"

Stereo TV: The Production of Multi-Dimensional Audio Roman Olearczuk

For the retailer nearest YOLI. or to order directly fi'om the publisher, call 800-428-SAMS. In Indiana. Alaska, and lla~vaii call 317-298-5699.

BOOK FOR SO ENG cERS

THE NEW AUDIO CYCLOPEDIA

Glen Ballou Editor

#f HOWARD W. SAMS &,COMPANY

A Division of Marmil/an. /nc,

4300 West 62nd SCref'l

Indianapolis. Indiana 46268 l SA

© 1987 by Howard W. Sams & Co. A Division of Macmillan, Inc.

FIRST EDITION THIRD PRINTING-1988

All rights reserved. No part of this book shall be reproduced, stored in a retrieval system. or transmi tted by any means, electronic, mechanical, photocopying, recording, or otherwise, without written permission from the publisher. No patent liability is assumed with respect to the use of the information contained herein. While every precaution has been taken in the preparation of this book, the publisher assumes no responsibility for errors or omissions. Neither is any liability assumed for damages resulting from the use of the information contained herein.

International Standard Book Number: 0-672-21983-2 Library of Congress Catalog Card Number: 85-50023

Acquisitions Editor: Charlie Dresser Editors: Pryor Associates & Sara Black Interior Design: Don Herrington Illustrator: William D. Basham Cover: Design-Meridian Design Studio, Inc.

Embossing-Shirley Engraving Co .. Inc. Photography-Visuals Unique

Composition: Graphic Typesetting Service, Los Angeles Indexer: James M. Moore

Printed in the United States qf America

iv

CONTENTS

PRE-F ACE ..................................................................................... .................... ,. .............. "........ .............. III .. ,. ., .. .. .. .. .. .. .. '" .. • .. ., ix

CONTRIBUTORS ............................................................. " ....................... III ...... " ...... 'II III ................ 11/1 .... '" .. '" ......... III' '" .. " .............. '" .. '" ,. • xi

PART I-ACOUSTICS

CHAPTER 1 FUNDAMENT ALS OF SOUND", .. '" .. '" .. '" .... '" .. '" .................... 1t ........ til .............. '" " 'III .................................... ,. ........ , til .. '" .. .. • .. .. .. 3

F. Alton Everest CHAPTER 2

PSYCHOA COU STIes ......... " .............. til .................. '" ......................... '" .................... 'II '" ................................ '" .. .. .. .. .. .. .. .. .. .. .. .. .. • 23 F. Alton Everest

CHAPTER 3 ACOUSTICS OF SMALL ROOMS .................... til .... '" .................... '" .............................. ., ............ '" ............ '" '" III .. " .. .. .. • .. .. .. .. .. .. 41

F. Alton Everest

COMMON FACTORS IN ALL AUDIO ROOMS

F. Alton Everest

CHAPTER 4 ........................................... IJI' ................................ ,. .... til ................... " .. .. 61

CHAPTERS ACOUSTICAL DESIGN OF AUDIO ROOMS .............•.............................................. 93

F. Alton Everest CHAPTER 6

RECORDING STUDIO DESIGN ...................... " .• *' ... , ...... ,. ................ " *' " •• " ••• " .... '" .. '" .. *' .................. " ..... II' • '" .. '" ................... '" ... ... 119 F. Alton Everest

ROOMS FOR SPEECH, MUSIC, AND CINEMA

Rollins Brook and Ted Uzzle

CHAPTER 7 ......... ,. ....... ,. ................................................................... " ... " ........... .. 155

CHAPTERS ACOUSTICS OF OPEN PLAN ROOMS ...............••.••••........•..........•.....•.•.•.........••... 199

Rollins Brook

v

vi CONTENTS

PART 2-ELECTRONIC COMPONENTS FOR SOUND ENGINEERING

CHAPTER 9 RESISTORS, CAPACITORS, AND INDUCTORS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Glen Ballou CHAPTER 10

TRANSFORMERS, .... , . " .. , .. " . " ... ,. ..... , ,. ... , 'II , 'III " 'III ... 'III ... II ..... , ...... , .......... , ......... ,. , ...... , ......... II ,. ....... , ........ ,. .. " , .. .. .. • • .. .. 227 Glen Ballou

CHAPTER 11 TUBES, DISCRETE SOLID-STATE DEVICES, AND INTEGRATED CIRCUITS......................... 247

Glen Ballou CHAPTER 12

HEAT SINKS, WIRE, AND RELAYS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Glen Ballou

PART 3-ELECTROACOUSTIC DEVICES

CHAPTER 13 MICROPHONES .... , ..... " .. " ....... " .. " .......... " ................ " ..... "" ............. '* ,. ,. ...... , '" " .... ., .. ,. .. '" ...... '" .. , , ... ,. , .. , .. , .. , .. , , , '" .. , .. , .. , , • 111 111 .. 315

Glen Ballou

CHAPTER 14 LOUDSPEAKERS, ENCLOSURES, AND HEADPHONES .................................... . . . . . . . . . . . . 405

Cliff Henricksen

PART 4-AI1DIO ELECTRONIC CIRCUITS AND EQUIPMENT

CHAPTER 15 AMPLIFIERS ... , , .. , .................. , , ......... , ..... , ............... , ..... .................. ,. ..................... ,. ..... '* ............. '" '" '" ., , ... " ... , ,. , ... , , , ... , '" , " , , 489

Gene Patronis Jr. and Mahlon Burkhard

CHAPTER 16 ATTENUATORS .............. , .......................................................................... ,., ........ 545

Glen Ballou CHAPTER 17

FILTERS AND EQUALIZERS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569 Glen Ballou

CHAPTER 18 DELAY ......... " ... " ... " .... " " " .. " " .. " .... " . ,.. II .................. '* " ............ '* .. " .. " II- , .... 'It " '* " .......... " ...... '* ........ , ...................... .., " " " • " " I 613

Mahlon Burkhard CHAPTER 19

POWER SUPPLIES ............ " .... '* " '* .......... " ... " ................ '* ...... '" .. '* ........ " '* '* ................ '* '* '* ................................ " .. " .. " " " " .. " .. " " , , 629 Glen Ballou

CHAPTER 20 CONSTANT- AND VARIABLE-SPEED DEVICES. . .. .. . . . . . . . . . .. . . . . .... . . . .. . . .. .. . . . . . . . . . . . . . . . . . .. 669

Glen Ballou

CONTENTS ....

VII

CHAPTER 21 VU AND VOLUME-INDICATOR METERS AND DEVICES ............................................... 683

Glen Ballou

CHAPTER 22 CONSOLES AND SYSTEMS .... '" ........ " .. '" . " ............. '" '" ........ ,. ..... '" '" ....... '" '" '" ........... *" .. '" ....... '" • '" '" '" ..... " .. '" .. '" .. .. .. .. .. .. 693

Steve Dove

PART 5-RECORDING AND PLAYBACK

CHAPTER 23 DISK RECORDING AND PLAYBACK .................................................................. 823

George Alexandrovich

CHAPTER 24 MAGNETIC RECORDING AND PLAYBACK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . 933

Dale Manquen

CHAPTER 25 DIGITAL RECORDING AND PLAYBACK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977

Dale Manquen

PART 6-DESIGN APPLICATIONS

CHAPTER 26 SOUND SYSTEM DESIGN" . 110 ........ '" " ... '" '" , '" '" ........ ;; ... '" '" '" .. '" ....... '" ,. '" '" '" ......... '" .. '" .. '" .. " .......... '" .. " • '" '" .............. '" '" .... '" • .. 995

Chris Foreman CHAPTER 27

SYSTEMS FOR THE HEARING IMPAIRED. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1091 Rollins Brook and Lawrence Philbrick

CHAPTER 28 THE BROADCAST CHAIN ........ 'III .. '" .......... It .......... '" ......... '" '" ............ '" .... III '" • " ............ '" .... " '" .... " ............ '" • '" '" ...... '" '" II- ........... "" 1101

Douglas Fearn

CHAPTER 29 IMAGE PROJECTION ........ '" .. '" .... " '" .. '" " .. " " ......... '" '" '" .... " '" II- '" .. " .. '" '" .. '" '" '" III .. '" ........... '" .......... '" • '" ............. '" .......... If ..... II- .... " .. "'.. 1119

Glen Ballou

PART 7-MEASUREMENTS

CHAPTER 30 A LTDIO MEASUREMENTS .......... II- ••••• '" • '" ........... II- .. '" '" •• '" • '" ...... '" '" ............... '" • '" , .. '" '" ...... Ii- ... II- ... '" ••• II- 1147

Don Davis

CHAPTER 31 FUNDAMENTALS AND UNITS OF MEASUREMENT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1191

Glen Ballou

INDEX •.......... « I Ii"" I ........ , ......... ,. ........ ,. .................... ,. "' ................ '* ...... , .................... "' ....... '" 1227

PREFACE

Our understanding of sound and our methods of producing. reproducing, changing. con­trolling, reinforcing, and measuring it are improVing with the advance of technology. The Handbookfor Sound Engineers: The New Audio Cyclopedia combines years of technical infor­mation and technological development into a comprehensive reference book. To compile this book, the expertise of many people was caJled upon. The result is a reference volume that covers seven areas: acoustics, electronic components. electroacoustic devices, audio electronic circuits and equipment, recording and playback, design applications. and measurements.

This book begins with the fundamentals of sound and its psychoacoustic effects on humans. With a good foundation of basics, we proceed to voice coloration and how it is affected from room to room depending upon a number of factors, such as the room construction and shape. Rooms for speech are designed for intelligibility, but rooms for music require very different characteristics, because blend Is more important than intelligibility. Multipurpose rooms must be designed to satisfy both speech and music. Studios and control rooms are getting more attention recently with the new LEDE® rooms and time-aligned loudspeakers. AU of this and more is discussed in detail in Part 1.

Microphones and loudspeakers are discussed in Part 3. The type, pickup pattern, and sen­sitiVity of a microphone determine its use and placement for sound reinforcement and re­cording; therefore, it is important to understand the basiCS of microphones, how they work. their various pickup patterns. and the proper method of determining sensitivity and frequency response. Wireless and PZMicrophones, are also discussed in detail.

The chapter on loudspeakers covers building. use, and standard test methods to measure them. The indiVidual components of a loudspeaker and their interrelation are discussed in detail for the engineer. Constant directivity horns, crossover devices, and Thiele enclosures are also included.

With the advent of solid-state deVices and digital circuitry, sound system electronics has come of age. Automatic microphone mixers and computerized consoles have changed the way sound is mixed. High-power output devices have produced stable, high-power and versatile ampllfiers, and digital circuitry has produced low-noise time delays and special-effect devtces. The Handbookfor Sound Engineers: The New Audio Cyclopedia discusses these new circuits along with the still used standard and speCial cirCUits.

Disk and magnetic recording and p1ayback have changed considerably in the past few years. particularly with respect to noise and distortion. Electronics has improved in reJiability and headroom. The introduction of digital circuitry, and improved transports and turntables has led to greater stability and less rumble. A knowledge of basiCS and special circuits is reqUired to properly serVice this eqUipment, which is discussed in section 5 .

. IX

x PREFACE

The design of sound systems has changed tremendously with the new electronics. constant directivity loudspeakers, and latest test equipment. Systems can be single source, multiple source. distributed, or time delayed, all with their own particular design problems. These situations are covered. in addition to proper installation techniques and how to design for best articulation, frequency response, coverage, and signal-to-noise ratio through the use of various types of loudspeakers. microphones, and electronics.

The new integrated circuits, digital circuitry. and computers have given us new, sophisti­cated test gear unthought of ten years ago. The TEF (time-energy-frequency) analyzer developed by Richard Heyser and designed and built by Crown International has changed the way sound is measured. It allows us to measure in real time in a noisy environment and measure with an accuracy never before realized. What to measure, the meaning and relevance of measurements. and the new instrumentation are thoroughly covered.

The understanding of sound. sound reinforcement. and acoustics can be attributed to thou­sands of people working in the field: however. we must give credit to those who, through their understanding of the problem. their ability to work out the solution, and most importantly their willingness to share it. have truly been modern-day pioneers. Lord Rayleigh. Thomas Edison, Wallace Sabine. Harry Olson, Leo Beranek, Harold Lindsay. Richard Heyser. and the dedicated, knowledgeable authors of Handbookfor Sound Engtneers: The New Audio Cyclo­pedia who were willing to give of their time to share their forte with the world are foremost on this list and I wish to thank all the authors for their contributions to this book and all the others who supplied these thoughts and comments.

I especially want to give my thanks to Don and Carolyn Davis. Their belief in me and this book and their special attention when things were looking down is a true example offriendship and synergy. Each newsletter they produce under their company. Syn-Aud-Con. starts. "I met a man with a dollar, we exchanged dollars. I still had a dollar. I met a man with an idea, we eXChanged ideas. now we each had two ideas." With this thinking, the field of sound will be better understood by all. the result being giant steps forward.

I also wish to thank my wife Debra. who spent as much time at the word processor as I did at the desk and most importantly was constantly there to encourage and drive me.

GLEN BALLOU

CONTRIBUTORS

GEORGEALEXANDROVICH

hokjs 17 Ud,n

GLEN BALLOU

was res,po,nslble design

roonw

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artl!:!e::!

nt'Trs (

t ranSreJ~red llTI&11r K'V'? II (; 0 JJl ~

tnn oolrllerell('e rnnms,

aUencted sel1nlnars on

ROLLINS BROOK

l'OfnmUIIICiUlYln:S frm:n

as broad(castlllg a coillnll'llst wrUl ten a nUlrnra~r

a valrleltv

MAlILON D. BURKHARD

berrn J;%Jrth,p I It

two wrlting gf(~lIPS for tbr lEe Terfm:lral Coml1rlltltee.

DONALD B. DAVIS

D~,vl!" with more U I"'"

wlwCmsi~.mS~~~,jllc~ldln'~I·~~tsIS~~tI~~nl,

and Carolyn Da\~ Ita"e ollavr:d mlcrophony. the LI\:e~ll;;nd

CONTRIBUTORS xiii

te<:hrllque of control room design, and the pioneer llc1en;slng lilevserlClii 'J'_h TEFl) measurtng SV!ltelrn now

manufactured Crown International, Inc. They are currentlly elrlIJlged new n~cOJding In as as he,lvtllv

sound engineering seminars, is the author three Acoustical Tests and Measlu,."m~~nt!i. ",ouna SlIlli'teln E'nghlE:'€rl!ng II:tll~indhorf:d

and How latUTr' having over /&/&;i3. u'VU (;oples. <:>UlAIlU SYlitel'l'1 E:nglnf!elrlng textlll10K used In teal:hlrlg el'e!troacl)Usllc U"''''J;;,U plrliclUcfiS at :syn·Aud..con sound engineering seminars

written hundreds of dealing "",rin, electrolitXlUISUCS, aUIlIo. and sound IcllJdlng many papers at culrlv(!ntlerls "UWlU E:nglnc:cdng Motion Picture

Tel,evl.slcln Engineers, the Acuustlcal Sllicle!!y AlIlfid!;:'l.

STEVE DOVE

King James ("n!lp,,,,"

dubious • "";;Il,,,",,

for od1lfrs. SIIf\lfI tI."njolned AllI:e StarlCOlll. pro-audio as a de,s,lgnflr.

has been slg.nifl,clIllt

more CUlnplltc<!ile(I" actf~d as t«lhnlcal aa}U~IUC con~

studios, lnt:Q~f:IrS. ar"",, a nUimlJer also iii author tlelde.

mrflr 50 J)apel'S Hn;mp and Stl.U:U,O.

WOmen

F. ALTON EVEREST

senior thlesls proiflct on

was nf:!!.er

Navy. whlfre

on

au,rllo train In\! cuurse. :["I'.'"8;ln", En~:lnCl!rS. II sellilOI[

a me Imber

DOUGLAS W. FEARN

hol,dsan

CHRIS FOREMAN

Inan

Chl'18 hullds a

'l"piL.Ill., rF()rRD A. HENRICKSEN

Jelrse,,!/, a

an on a bonk

new prc.duct':l Inal

dh'eclro com~ helPf:d o~I,gn con{'cl'l

a contributor chairman

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DALE MANQUEN

EUGENE T. PATRONIS. JR.

Unlokl1aVlcn N:atlcloal Latloraltmy as a res'ean:n

Pa:tronls scrv~ as an irK!le)denaellt

a member

mOUZZLE

an hN,n a cOflSullull:

PARTl

CHAPTER 1

Fundamentals of SOl'nd

by F. Alton Everest

1.1 DUAL NATURE OF SOUND ..................................................................... 5 1.2 TRANSMISSION OF SOUND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 TYPES OF WAVE MOTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 NATURE OF SOUND WAVES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 PERIODIC WAVE RELATIONSHIPS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.6 SPEEDOFSOUND.................................................................................. 7 1. 7 FREQUENCY AND WAVELENGTH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B I.B WAVEFRONTS AND RAYS. . .. . . . .. . . . ... . . . . . . . . . . . . . . .. . . .. . . . . . . . . . . .. . . . . . . . .. . . . . . . . . . . . . . . 9 1.9 REFLECTI ON OF SOUND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.10 REFRACTION OF SOUND ................................................ <> • • • • • • • • • • • • • • • • • • • • • • 9

1.10.1 EFFECT OF AIR TEMPERATURE ON SOUND PROPAGATION ............................ 10 1.10.2 EFFECT OF WIND ON SOUND PROPAGATION ............................................ 10

1.11 DIFFRACTION OF SOUND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.12 SUPERPOSITION OF SOUND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.13 ACOUSTICAL COMB FILTERS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 12 1.14 INVERSE-SQUARE LAW...... .. .......... .. .... .. .. . . .... . .... . .. .. .. ... . . . .... .... ..... . ..... . 14 1. 15 DIMENSIONAL ANALYSIS ...................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1. 16 DECIBEL NOTATION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.17 EQUIVALENCE OF LOGARITHMIC AND EXPONENTIAL FORMS ....................... . . . . . . 1 7 1.18 INVERSE-DISTANCE LAW AND THE DECIBEL......... ...... ..... ....... ....... ..... ... .. ... . IB 1. 19 COMBINING DECIBELS .................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1B 1.20 SPECTRUM LEVEL AND THE DECIBEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 1.21 MATHEMATICS OF THE OCTAVE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . . . . . . . . . . . . . . . . . . . . . . . 20 1. 22 WEIGHTING NETWORKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 REFERENCES ..................... '" ................................................ ., '" .. '" .................... '" .. '" ......... '" '" ... .. . . . ... .. . .. . .. .. . . .. .. .. 21 ADDITIONAL BIBLIOGRAPlIY ....................................................................... 21

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FUNDAMENTALS OF SOUND

1.1 DUAL NATURE OF SOUND

Sound has a dual nature: it may be considered a phys­ical disturbance in a medium such as air, or it may be considered a psychophysical perception resulting from nerve impulses stimulating the acoustic cortex of the brain. In audio we are vitally concerned with both. The ear itself determines the quality of sound signals, but the sound is carried to the ear through physical stimuli. The matter of the complex relationship between stimulus and sensation is treated in Chapter 2. dealing with psycho­acoustics. In this chapter we are concentrating on the physics of sound.

1.2 TRANSMISSION OF SOUND

For sound to be transmitted from one place to another. a medium is required that has elasticity and inertia. Air has these vital characteristics, as do steel. water, con­crete. and many other substances. When an air particle is booted by a diaphragm. it moves, passing on momen­tum to adjoining particles as it strikes them. The original air particle Is then pulled back toward its equilibrium position by elastic forces residing in the air. Any partic­ular air particle vibrates about its equiJibrium position. receives momentum from collisions, and passes on momentum to other particles, which pass it on to others. and so on. The wind sends a wave traveling through a field of grain, but each head of grain merely Vibrates back and forth on its stem. Sound is propagated through the air by virtue of elastic and inertial forces acting on the air particles. each of which stays close to home.

1.3 TYPES OF WAVE MOTION

When we think of wave motion, water comes immedi­ately to mind, and water waves have traditionally been aSSOCiated with demonstrations of acoustical wave con­cepts. However, we will be spared the throwing of stones into placid pools and get on with the mechanics of wave motion. We have seen that all wave motion is based on the vibration of elemental particles and that these par­ticles stay close to their neutral positions in the process of sending sound waves on their way.

Water waves are produced by particles in Circular orbits. Surfboard riders at the crests of waves move toward the shore. but if they get "wiped out." they discover that the water beneath the waves is moving away from the shore. The water particles follow Circular orbits, as deSCribed in Fig. I-IA. This Circular motion is a form of simple har­monic motion with particle displacement plotted against time. describing a sine wave.

Transverse wave motion is depicted in Fig. I-I B. In this case the particle vibrates in a plane at right angles to the direction of travel of the wave. Stretched strings used in

5

many musical instruments vibrate transversely as the waves are propagated toward the ends of the strings. It is interesting (but not particularly pertinent) that light. heat. and radio waves in free space travel by transverse vibrations of the electric and magnetic fields.

Our primary interest centers on sound waves that are propagated by longitudinal vibrations of air particles, I.e .. by vibrations parallel to the direction of sound travel as in Fig. I-Ie.

All three forms of particle vibration depicted in Fig. 1-1 are simple harmonic motion. The sine wave is a nat­ural outgrowth of all three types of motion. Particles vibrating in transverse and longitudinal orbits are of pri­mary interest in audio, particularly the longitudinal form that applies to the air medium.

1.4 NATURE OF SOUND WAVES

Sounds in air are commonly produced by the vibration of diaphragms (such as loudspeakers or headphones), vocal cords. instrumental strings. jackhammers. or some other solid material. In Fig. 1-2 let us conSider as our vibrating body a hypothetical piston, which is driven by a crankshaft and connecting rod. The piston, as shown, is in its extreme position to the right. As it moved to this position. the air particles immediately in front of it are crowded together. As the piston moves back to its oppo­site extreme {leftL a partial vacuum is created as the air particles are spread apart. This disturbance of air parti­cles close to the piston is passed on to adjoining particles, as the momentum imparted to one particle is passed on to another through collision. Each particle vibrates about tts neutral position as the wave travels on. Because this piston moves in simple harmoniC motion, we expect a sine wave of air pressure to be formed.

The crowding together of air particles constitutes an increase of pressure (compression); their spreading out. a decrease of pressure (rarefaction). Because these air particles are part of the "ocean of air" in which we live. these increases and decreases of pressure are superim­posed on the particular prevailing atmospheriC pressure, as read off a barometer. These modulations are very small. The weakest sound the human ear can hear [about 20 micropascals (f.LPaJ] will create a pressure ripple only one five-thousandth of a millionth of the atmospheric pres~ sure. Microphones respond to the ripples only, not to the static atmospheriC pressure.

1.5 PERIODIC WAVE RELATIONSHIPS

The waves of sound pressure of Fig. 1-1 are called peri­odic waves because they repeat over and over. Periodic waves need not be sine waves-only repetitive waves. A few definitions pertaining to periodiC waves are in order as we refer to Fig. 1-3. The peak value is easy to read from

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• 5

+

4 G --- 1-1 _______________ ~..011!::__ DIRECTION OF WAVE TRAVEL IS 4 PERPENDICULAR TO THE BOTTOM OF THE PAGE

(B) Transverse particle motion such as in stretched strings.

2

+

.... z: ..... :IE ... .. .. ,.., 2 ~O ... .. " "'", C

3 ....I A.. en TIME -

J is

DISPLACEMENT +

5

DIRECTION OF WAVE TRAVEL --

4

(C) Longitudinal particle motion as in sound waves in air.

7

5

Figure 1-1 Orbital motion of particles in the medium differentiates the types of motion.

ACOUSTICS

an oscilloscope trace, but only a few instruments can reg­ister it. Peak to peak is, of course, twice the peak value if the waveform is symmetrical.

doing work. It is what is commonly called the rms value. To remove some of the mystery, we shall follow through on the meaning of rms (root mean square).

With an alternating electric current, flowing first in one direction and then in the opposite direction, or an alter­nating sound-pressure wave, with positive (compression) and negative (rarefaction) loops, how can such con­stantly changing signals be represented by a single fig­ure? The answer is that the e1fecttve value must be deter­mined. The effective value is related to producing heat or

In Fig. 1-4 a definite (but arbitrary) amplitude scale has been introduced. The amplitudes at a. b, c, d, e. and f can be read off for the positive loop and negative ampli­tudes at a', b'. c', d', e', and f' can be read off for the negative loop. The following steps are then taken:

1. Square each amplitude of the positive loop.

FUNDAMENTALS OF SOUND

+ ATMOSPHERIC PRESSURE

SOUND / PRESSURE 0 t-----"I:-----+----4r----r----'---

Figure 1-2 A piston as an illustration of wave motion.

+

ONE CYCLE ONE WAVELENGTH --j

ONE PERIOD I

PEAK ~----~~-~~~---~~ TO

nME-

~_JK

Figure 1-3 A periodic wave. In this case, a sinusoidal wave described in temporal terms by

frequency (reciprocal of period).

2. Square each amplitude of the negative loop. Since a minus quantity squared becomes positive, the negative loop values give the same results as though the broken line positive loop were followed, which means that we are duplicating the positive loop.

3. Add all squared values together.

4. Find the average (or mean) of all squared values: divide the result of step 3 by the number of values squared.

5. Take the square root of the mean of step 4.

Following these steps gives us the rms value (the square root of the mean of the sum of the squares = root mean square). This rms value is the effective value of the sine wave of Fig. 1-4. Electrical power is proportional to the square of the rms voltage, and acoustic power is propor­tional to the square of the rms sound pressure.

Most meters for measuring alternating voltage or sound pressure have dc movements with a full-wave rectifier attached. Thus. they respond to the average. not the

+1

o abcdef

-1

/-.

I ' I \ I \

I \ I \ I a' b' c' d' e' f' \

7

Figure 1-4 Finding the rms (root-mean-square) va1ue of a periodic wave by measuring instantaneous

ampl itudes.

effective or rms value. However, they are almost univer­sally calibrated in terms of rms, which means that they are accurate only for sine waves. The greater the depar­ture from the sine waveform. the greater the reading error. Thermocouple instruments and those with carefully designed networks read rms directly irrespective of the waveform. The following relationships between rms, peak. and average hold true for Sine waves:

or

and

or

rms = peak/V2

= 0.707 x peak

rms = (1T/2V2) X average

1.11 x average

peak = v2 x rms

= 1.414 x rms

peak = (1T/2) x average

= 1. 5 7 x average

1.6 SPEED OF SOUND

(1-1)

( 1-2)

( 1-3)

( 1-4)

The words speed and velocity are often equated. but in the strict technical sense. these terms are not the same. Speed means rate of change of position in units such as miles per hour. feet per minute. meters per second. and so on. Velocity of a body is a vector quantity. having the same magnitude as its speed but including also the direc­tion of motion. If no directional information is at hand. speed is the accepted term. If direction of propagation is involved, velocity is the proper term.

Mersenne (1588-1648) used Galileo's (1564-1640) pendulum to measure the speed of sound in air. obtain­ing a value of 1038 ftls. 1 Members of the French Academy

8

Table 1-1. Speed of Sound in Various Media

Media Meters/Second Feet/Second

Air, 21°C 344 1129 Water, fresh 1480 4856 Water, salt, 21°C,

3.5% sal inity 1520 4987 Plexiglass 1800 5906 Wood, soft 3350 10,991 Fir timber 3800 12,467 Concrete 3400 11,155 Mild steel 5050 16,568 Aluminum 5150 16,896 Glass 5200 17,060 Gypsum board 6800 22,310

From Bart lett.4

in 1738 conducted the first accurate experiments by using cannon fire and measuring the difference between the arrival of the flash and the sound. They came up with a value of 337 mls (1106 ftls) for dry air at 0°C.2 Better control of the measuring process has resulted in an aver­age of 17 determinations3 as 33. 145 + 5 cmls or 1087.42

O. 16 ftls for audio frequencies. air temperature of O°C. one atmosphere pressure, CO2 of 0.03-mol-percent con­tent, and 0% water content. For practical purposes and under normal conditions. the speed of sound in air and various other media is given in Table 1-1.

The speed of sound in air is commonly rounded off to 1130 ftls for normal conditions. which is slow compared to light and radio waves (186.000 mils) but comparable to the speed of a .22-caliber rifle bullet (about 1000 ftls). Atr speed in air-conditioning ducts in studios is usually held below 500 ftlmin (8.33 ftls), which is less than 1 % of the speed of sound. This fact leads us to the conclusion that noise travels equally well upstream or downstream 1n the ducts. A 20°F change in air temperature results in about 2% Change in speed of sound.

1.7 FREQUENCY AND WAVELENGTH

Let us imagine that a sound wave is traveling past us and that we are equipped with "instant replay" and slow­motion facilities. As the wave goes by. we can sense the compression peaks and the rarefaction troughs of air pressure. With a special scale. we measure the distance between successive peaks (wavelength) and the time it takes for 1 wavelength to pass. This time is related to the wavelength and speed of sound according to

t = Alc

where, t is the period for one cycle in seconds. A is the wavelength in feet. c is the speed of sound, which is 1130 ftls.

( 1-5)

ACOUSTICS

Since one complete cycle passes in time t. the fre­quency. or number of cycles passing in a second is

where.

f lit

= ciA

f 1s the frequency in cycles per second (hertz).

( 1-6)

As frequency is determined by the vibration of the source and is thus the primary quantity. it is useful to express wavelength in terms of frequency:

A = 1130/f 0-7)

This simple statement will be used many times as we consider the dimensions of our sound-sensitive rooms, or objects in those rooms, in terms of the wavelength of the sound. Fig. 1-5 is a handy graphical solution of Eq. 1-7.

Figure 1·5 A graphic solution of Equation 1-7 showing the relationship of the wavelength of sound in air to

frequency (speed of sound taken as 1130 ft/s).

FUNDAMENTALS OF SOUND

1.8 WAVEFRONTS AND RAYS

A wavtifront is defined as a line of pOints in the medium that are at the same part of the vibration cycle (in phase). This definition means all points on the wavefront are equidistant to the source. Waves emitted from a point source have spherical wavefronts, as shown in Fig. 1-6A. At a relatively great distance from the source, a section of a spherical wavefront approximates a plane surface (Fig. 1-6B). Plane and spherical wavefronts are of primary interest and concern in acoustics although other fronts can be produced under certain circumstances.

A ray of sound is the path of an element of the wavefront and, if not deflected in some way, is always perpendicular to the wavefront. as in Fig. 1-6.

We can l1ken a wavefront to a line of marching people. Each person walks radially away from the source in a spherical wavefront, but in a plane wavefront the people all walk in the same direction.

SOURCE --.

(A) Spherical wavefronts.

FROM DISTANT SOURCE

RAY

(B) Plane wavefronts.

Figure 1-6 A pOint source in free space sends out spherical wavefronts that tend to become plane

wavefronts at great distances.

1.9 REFLECTION OF SOUND

If the wavelength of sound is small compared to the dimensions of a smooth, hard surface. reflection takes place. Like light. the angie of incidence of sound onto a plane surface equals the angie of reflection, as illustrated in Fig. 1-7 A. A convex surface, such as Fig. 1-7B, scatters the rays of sound. A good example of this is the so-called "polycylindrical diffuser" sometimes used in acoustical treatment of studios. The concave surface of Fig. 1-7C tends to focus sound. A parabolic surface focuses sound very accurately. Concave architectural shapes in audi­toriums can create grave acoustical problems.

No discussion of reflection for those interested in re-

(A) A plane, solid surface.

(e) A concave surface.

I .J1'

- ... -::-----00+---..-" ---------.. ----:.---~- -.. --

""': ------ 00+---------- .....

(B) A convex surface.

-" ",-...",

I _-"""' ...... --~-....-----'" -

..--- 90"

(D) A corner reflector.

9

Figure 1-7 Plane wavefronts of sound striking variously shaped surfaces.

cording audio signals is complete without calling atten­tion to the existence of corner reflections in rectangular rooms. Normal (right angle) reflections from the flat walls are almost intuitively sensed; the corner reflections are a bit more obscure. Referring to the long dashed lines of Fig. 1-7D, representing rays of sound. it is seen that the incident ray is sent back toward the source from the reflecting surfaces forming a 900 corner. At any point in the room, this reflection is back toward the source as illustrated by the broken lines of Fig. 1-7D. Not only is this true for the two-wall corner reflectors. it is also true for corners formed by the wall surfaces and ceiling. and the wall surfaces and floor. Fortunately, all these corner reflections include two or more surface reflections which tend to reduce their amplitude. On the other hand. effi­cient reflections at grazing angles are often involved.

Picture a person in the central part of a recording stu­dio whose voice is being recorded. In treating the room. we must consider the possibility of four "slapback" echoes from the four walls. four from corners at microphone height, four from upper corners. and four from lower cor­ners-sixteen in all.

1.10 REFRACTION OF SOUND

Table 1-1 listed the wide range of sound speeds in dif­ferent media. As sound waves pass from one medium into

10

DENSITY OF MEDIUM 1 IS d,

DENSITY OF MEDIUM 2 LESS THAN d.

DENSITY OF MEDIUM 3 IS d.

(A) The sound goes from a medium of density D to one of lower density, then back into a medium of density D, restoring the sound ray to its original

direction.

NIGHTTIME DAYTIME

CODL AIR (LOW VELOCITY)

COOL AIR (LOW VELOCITY)

iJl7lJ//l7l7lffnffjj///I//i///I//////u/////mrl/ff///////i//I/////Iff//ffl//i///l/iTI»//Ih

(B) The effect of gradual transitions in density in bend­ing the path of a plane wave.

Figure 1-8 The path of a sound is reflected (bent) as it goes through an interface between media of different

densities.

another, there will be no refraction or bending of the direction of propagation if the speed of sound is the same in both media. If, however. sound passes from a medium of one density into a medium of greater or lesser density. the direction of propagation will be Changed.

In Fig. I-8A sound travels from dense medium 1 of den­sity d into medium 2 of lower density and then into medium 3. which has the same density d as medium I. A close examination of what happens at an interface gives us the means of determining which way the ray will be bent. The plane wave incident on the left of Fig. I-8A is represented by straight lines separated by a wavelength. Line AC begins its sojourn in medium 2 at point A. While the incident ray travels from C to 0 in medium 1. it travels from A to B in medium 2. In the lower-density medium 2. the sound travels slower because sound speed Is pro-

ACOUSTICS

portional to density. The wavelength of the sound is shorter because wavelength is directly proportional to sound speed, Eq. 1-7, which causes the plane waves to go off in a new direction in medium 2. As the sound ray leaves medium 2 and begins to enter medium 3. we see that during the time the wave travels between points G and H and pOints E and F, propagation is restored to the original direction.

1.10.1 Effect of Air Temperature on Sound Propagation

In Fig. 1·8A the density transitions between media were abrupt, but this is not always true. Fig. 1-8B illustrates a common experience in the propagation of sound out­doors. Sound travels faster in warm air than in cold air. Temperature stratification of air layers near the earth is common. During early morning hours, the warmth of the earth causes the lower layers of air to be warmer than the upper layers. As a result. sound rays bend upward, as in the left sketch ofFtg. 1-8B. From the earth's surface. sound does not appear to travel as far because the sound energy is directed upward. During the day the sun causes the upper air layer to be warmer than the lower layer. result· Ing in a bending of sound down toward the earth. From the earth's surface. sound appears to travel greater dis­tances later in the day. Hot air tn the upper part of an auditorium would tend to bend sound rays down to the audience, but the effect Is modest over short distances.

1.10.2 Effect of Wind on Sound Propagation

Stratification of air temperature is one factor affecting propagation of sound outdoors; wind is another. Ifwind moves the air particles involved in propagating sound. the velocity of the wind, combining vectorially with the velocity of sound. affects the direction of travel of sound rays. A 20-mph wind (29.3 ft/s) is only 2.6% of the speed of sound ( 1130 fUs). which does not seem like much, but such wind can have a noticeable effect on the propagation of sound near the earth.

Sound from an elevated outdoor loudspeaker traveling with the wind is refracted down toward the earth; thus. the acoustic level is sustained to greater distances. Sound from an elevated outdoor loudspeaker aimed into the wind will not carry as far. In this case the sound is refracted upward over the heads of the audience. Lowering the elevation of the loudspeaker is no solution to wind effects as other effects come into play to limit its range.

Wind of fluctuating velocity creates effects far more dev­astating on an outdoor sound system. Here the sound from the loudspeakers seems to the distant audience to fluctuate in volume as the beam is bent upward and downward as well as left and right. Rapidly varying effects

FUNDAMENTALS OF SOUND

such as these are more readily perceived than more con­stant ones. such as temperature effects. The perfor­mance of an outdoor sound system on a cold. calm morn­ing may be quite different from its performance on a hot. windy afternoon.

1.11 DIFFRACTION OF SOUND

An ocean wave sweeps past the pilings of a dock almost as though the pilings do not exist. A large island in mid­ocean, however, offers more resistance. Calm seas would be found in its lee, even though waves would spread around each end. The length of a wave is as important for ocean waves as it is for sound waves. For a sound wave that is long compared to the size of an obstacle, the sound wave continues, seemingly unimpeded.

(A) The brick wall reflects high audio-frequency energy having wavelengths small compared to wall

dimensions.

11

At 50 Hz the wavelength of sound in air is about 23 ft. Will a brick wall lOft high shield a house from traffic noise components around 50 Hz? Fig. 1-9A sets up this situation. The source S emits sound that strikes the brick wall. Of course, the brick wall reflects most of the sound energy falling upon it, shielding the house from high­frequency componen ts of the traffic noise. The house is located in a shadow zone behind the wall. This shadow zone exists for high frequencies because the brick wall is large compared to the wavelength of sound; for such con­ditions rays of sound tend to act like rays of light.

For sound waves in the 50-Hz region and below. how­ever. there is an effect that bends sound into the shadow zone behind the brick wall. Huygen 0629-1695) enun­ciated a principle that states that every point on a wave­front acts as though it were itself a center of disturbance. sending out little wavelets of its own. These wavefront

REFLECTED WAVES____.

DIRECT I WAVEFRONTS I

\'

•

....- ------..",.

~~-~---~------~

----------

d+2x d+3x!2 d+X d+x/2

"'-FDCAL POINT

---- ... " -'I

(B) The zone plate has concentric openings so spaced that path lengths vary by integral wavelengths.

Figure 1-9 Diffraction of sound.

12

sources, such as P in Fig. 1-9A, send sound energy into the area behind the wall causing the shadow zone to be something less than "dark." Thus, the brick wall is quite effective in shielding the house from the high-frequency components of traffic noise, but it is less effective for low­frequency components that are "bent" by diffraction into the space behind the wall.

A curious example of diffraction is the zone plate of Fig. 1-9B. A series of concentric openings is placed so that, when the plate is midway between the source and the focal point, the path lengths vary by integral wavelengths that add in phase at the focal point.

Diffraction occurring around our heads affects the way we hear sounds. It affects the directional response of microphones and occurs at loudspeaker cabinet edges, leaving its imprint on performance. Diffraction effects are never very far away in audio systems.

1.12 SUPERPOSITION OF SOUND

The principle of superposition says that the same por­tion of a medium can simultaneously transmit any num­ber of different waves with no adverse mutual effects, which is often called interjerence. an unfortunate choice of words. If several sound waves travel simultaneously through a given region of the air medium, the air particles in that

WAVE 1

+ ..... Q

= S 0 A. :::Ii c

WAVE 2

RESULTANT

TIME ---

(A) Waves 1 and 2 of equal amplitude and in phase add to give twice the amplitude.

ACOUSTICS

region will respond to the vectorial sum of the displace­ments of each wave system.

The sketch of Fig. I-lOA is a highly simplified illustra­tion of the principle of superposition. If wave 1 and wave 2 arrive at a given air particle at the same time, how will the particle respond? If these two wave systems have equal amplitudes and are in phase, the air particle must respond to the resultant, which is of the same frequency but twice the amplitude. In Fig. I-lOB wave 2 has the same fre­quency and amplitude as wave 1 but is displaced in time a half-wavelength (1800 phase shift). The resultant of the two is zero as one cancels the other. The aIr particle serves wave 1 and wave 2 at this spot and at this instant by not moving at all.

1.13 ACOUSTICAL COMB FILTERS

When the two combining waves have different ampli­tudes, phases, and frequencies. a much more complex situation results, but the principle of superposition still holds. Acoustical comb filters are so common in audio work and are so devastating of quality that they deserve special attention. In Fig. 1-10 we combined identical sig­nals shifted in time relationships. In other words, we introduced time delay (phase lag) between waves 1 and 2 in Fig. I-lOB. If waves 1 and 2 are identical, but highly

..... + Q

= l-;:j

0 A. :::Ii c

~ + = l-

WAVE 1

WAVE 2

i! 0 1r------4t--~--+----L..-~ TlME-

..... + RESUL TANT

~ \ ::::i 01-------------A. :::Ii c TlME-

(B) Waves 1 and 2 of equal amplitude but 18(J' out of phase cancel, yielding a resultant of zero.

Figure 1-10 The extremes of superposition (interference).

FUNDAMENTALS OF SOUND

complex such as voice or music. we must consider what a time delay does down through the audible spectrum.

The phase lag ($) for any frequency (f) for any given time delay (t) is given by

( 1-8)

When two identical signals separated by a phase lag $ are added together. the amplitude of the sum depends on the phase lag. If the phase lag $ = O. the two signals are in phase. as in Fig. 2-10A. Adding two waves. each of amplitude A. gives an amplitude of 2A. If two waves. each having an amplitude A. are added together a half wave­length or 1800 (or 11' radians) out of phase, they cancel each other and the resultant amplitude Is zero. A general statement for adding two waves of identical shape and amplitude is given by4

AR = 12 cos ($/2)1 A

where. AR is the resultant amplitude, A is the amplitude of both wave 1 and wave 2. $ Is the phase lag between the two waves.

( 1-9)

The absolute value of 2 cos ($/2) is taken because the amplitude Is always positive.

Combining Eqs. 1-8 and 1-9 gives

AR = 12 cos 11'ftl A (1-10)

where, f Is the frequency in hertz. t is the time delay in seconds.

Note that the product 11'ft is in radians. not degrees. Note also the cyclic nature of the cosine term (cos 0 = 1, cos 11'/2 = 0, cos 11' = - 1, cos 311'/2 = 0, cos 211' = 1, and so on). Adding two identical waves with a delay of t sec­onds between them gives a response that is a series of sine-wave shapes (the same shape as cosine waves) with the negative-going excursion inverted. Response shapes for delays of O. 1. 0.5. and 1.0 ms are shown in Fig. 1-11 plotted on a linear frequency scale. At frequencies that bring the two waves into phase, the amplitude is doubled ( + 6 dB); when they are 1800 out of phase, they cancel giving a deep null. The basis of the term ucomb filter" is evident from these responses. The identical responses are plotted to the more familiar logarithmic frequency scale in Fig. 1-12.

Whenever the cosine term of Eq. 1-10 is unity. AR =

2A. Since we are considering amplitudes of voltage or sound pressure and not power, these peaks of amplitude 2A can be expressed in decibel form as

amplitude = 20 log ARIA

= 20 log 2

= +6.02dB

13

+10

'" /' " / co 0 .. \ I \ I I ...

"" z 2 -10 .~ .. - .. .,. \ I ! I ~ i ...

~ ::ao J ~ -20 I I .... ... ..

I -30 0 4 8 12 16

FREQUENCY - kHz

(A) Response for a delay of O. 1 ms.

+10

"'\ n f'~ n (~ ('\ 11'\ n '\ () co 0 ... I ~ ~ -10 ~

D.. ... ... .. ... ;: -20 c .... w ..

-30 0 4 8 12 16

FREQUENCY - kHz

(8) Response for a delay of 0.5 ms.

+10

~ " ~ /'\ " " " " n It " n n n n

co 0 ... I ... ... z 2 -10 ... ... .. ... ~

S -20 .... ..

-30 0 4 B 12 16

FREQUENCY - kHz

(e) Response for a delay of 1.0 ms.

Figure 1-11 Response shape for delays of 0.1, 0.5, and 1.0 ms.

20

I'

20

20

At frequencies at which the cosine term is zero, AR = 0 and cancellation results. The amplitude in decibels becomes

amplitude = 2010g0/A

= 2010g0

= -oodB

In practice this cancellation is closer to 20 to 40 dB rather than - 00,

Figs. 1-11 and 1-12 apply to any complex voice or music signal that is combined with itself and delayed by the indicated time. For a delay of 0.1 ms. a deep null at 5 kHz and another at 15 kHz are observed. At these frequencies

14

"" ... I

..... <I> z Q ... <I> .... "" "" ,.. ;:= .., -' .... ...

CD ."

I ..... <I> Z Q ... ..., .... '" .... :!: .... c ..... ..... ""

'" ... I ... ...,

z: 0 ... '" ..... "" ..... ,.. ;:=

"" -' .... ...

+ [0

0

-10

-20

-30 20

+10

0

10

-20

-30 20

+ :0

0

!

10

-[0

30 20

I

!

~~ ( r\ I

I \ I i

I

\ I \1

50 100 200 500 Ik 2k 5 k 10k 20 k

fREQUENCY - Hz

(A) Response for a delay of O. 1 ms.

~ r \ I' • ~ '" n • \ I \

\ 50 100 200 500 I k n Sk 10k (Ok

FREQUENCY - HI

(B) Response for a delay of 0.5 ms.

•

!

'\ rr\ f"\ n

i , ""-

\ i

!

!

50 100 100 500 L k 2 k 5 ~ 10 k 20 k

FREQUENCY - Hz

(C) Response for a delay of 1.0 ms.

Figure 1-12 Comb filter data from Fig. 1-11 plotted on logarithmic scales.

this O.I-ms delay places the delayed and undelayed sig­nals in phase opposition. and the null results. Between nulls the signals come into phase, and double ampl1tude results. Many more nulls occur within the audible band for a delay of 0.5 ms, and still more for l.O-ms delay.

Certain generalizations can be made

1. The spacing between peaks is always (lit) Hz.

2. The nulls occur when nft equals n/2. 3n/2, 5n/2, and so on.

ACOUSTICS

3. For long time delays, the distance between peaks is small.

4. Short time delays give greater peak separation.

The important question is, "How audible are the effects of the response of Fig. 1-I2T' Delays of these magnitudes can easily be experienced by recording speech as the talker walks toward a highly reflecting wall holding the micro­phone at a constant distance from the lips. The reflection of the voice from the wall combines with the direct signal at the microphone diaphragm. The reflection is delayed because of the greater distance traveled. One foot differ­ence of path length gives a delay of 111130 ftls = 0.9 ms, or 1. 13 ft corresponds to a I-ms delay. When the approach to the wall yields delays in the order of 1 ms, significant distortion will be noticed as the recording is played back. For greater delays, the null spacing becomes very small. and the primary effect noticed is the 6-dB increase in level at the peaks .

Bucklein5 in his study of the aUdibility of frequency response irregularities found that peaks had consider­ably greater effect on quality than valleys.

1.14 INVERSE-SQUARE LAW

Those active in audio have many occasions to apply the inverse-square law. We know that sound gets weaker as distance from the source is increased. Now all we have to do is find out how much weaker for a given increase in distance. To solve this we assume that a point source is radiating W watts into a free field. The sound energy flows out in all directions on spherical wavefronts. Let us con­sider the sound flowing outward within a certain solid angle, as shown in Fig. 1-13. Sound intensity is defined as the sound power per square centimeter. In Fig. 1-13 the intensity would be the number of watts divided by the total area of the sphere or

(1-11)

where. I is the sound intensity in watts per centimeter squared, W is the sound power of source in watts, r is the distance from the source in centimeters.

At a distance r 1 from the source,

At a distance r2 from the source,

(I-I3)

But since the same sound power flows through spheres at both r 1 and r2. Eqs. 1-12 and 1-13 are equal:

(1-14)