Microphone
`Book
`a+3“7a49,595,455=.LoteS
`
`APPLE 1017
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`John Eargle
`
`From mono to stereo
`} &to surround
`
`~— We(ence —
`smicrophonedesign
`and aL |
`
`APPLE 1017
`
`1
`
`

`

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`
`THE MICROPHONE BOOK
`
`Second edition
`
`2
`
`

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`
`THE MICROPHONE
`BOOK
`
`Second edition
`
`John Eargle
`
`AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD
`PARIS • SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO
`Focal Press is an imprint of Elsevier
`
`4
`
`

`

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`
`Focal Press
`An imprint of Elsevier
`Linacre House, Jordan Hill, Oxford OX2 8DP
`30 Corporate Drive, Burlington MA 01803
`
`First published 2005
`
`Copyright © 2005, John Eargle. All rights reserved
`
`The right of John Eargle to be identified as the author of this work
`has been asserted in accordance with the Copyright, Designs and
`Patents Act 1988
`
`No part of this publication may be reproduced in any material form (including
`photocopying or storing in any medium by electronic means and whether
`or not transiently or incidentally to some other use of this publication) without
`the written permission of the copyright holder except in accordance with the
`provisions of the Copyright, Designs and Patents Act 1988 or under the terms of
`a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road,
`London, England W1T 4LP. Applications for the copyright holder’s written
`permission to reproduce any part of this publication should be addressed
`to the publisher
`
`Permissions may be sought directly from Elsevier’s Science and Technology Rights
`Department in Oxford, UK: phone: (+44) (0) 1865 843830; fax: (+44) (0) 1865 853333;
`e-mail: permissions@elsevier.co.uk. You may also complete your request on-line via the
`Elsevier homepage (www.elsevier.com), by selecting ‘Customer Support’
`and then ‘Obtaining Permissions’
`
`British Library Cataloguing in Publication Data
`A catalogue record for this book is available from the British Library
`
`Library of Congress Cataloguing in Publication Data
`A catalogue record for this book is available from the Library of Congress
`
`ISBN 02405 1961 2
`
`For information on all Focal Press publications visit our website at:
`www.focalpress.com
`
`Typeset by Newgen Imaging Systems (P) Ltd, Chennai, India
`
`Printed and bound in the United States
`
`Working together to grow
`libraries in developing countries
`www.elsevier.com | www.bookaid.org | www.sabre.org
`
`5
`
`

`

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`
`CONTENTS
`
`Preface to the First Edition
`Preface to the Second Edition
`Symbols Used in This Book
`
`vii
`ix
`
`x
`
`50
`66
`
`117
`142
`
`1
`1 A Short History of the Microphone
`2 Basic Sound Transmission and Operational Forces on
`Microphones
`7
`22
`3 The Pressure Microphone
`4 The Pressure Gradient Microphone
`5 First-Order Directional Microphones
`91
`6 High Directionality Microphones
`7 Microphone Measurements, Standards, and
`Specifications
`105
`8 Electrical Considerations and Electronic Interface
`9 Overview of Wireless Microphone Technology
`10 Microphone Accessories
`152
`11 Basic Stereophonic Recording Techniques
`12 Stereo Microphones
`184
`13 Classical Stereo Recording Techniques and
`Practice
`194
`217
`14 Studio Recording Techniques
`15 Surround Sound Microphone Technology
`16 Surround Recording Case Studies
`271
`
`166
`
`243
`
`6
`
`

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`vi
`
`Contents
`
`17 A Survey of Microphones in Broadcast and
`Communications
`290
`18 Fundamentals of Speech and Music
`Reinforcement
`301
`19 Overview of Microphone Arrays and Adaptive
`Systems
`322
`20 Care and Maintenance of Microphones
`21 Classic Microphones: The Author’s View
`
`334
`338
`
`References and Bibliography
`Index
`373
`
`367
`
`7
`
`

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`
`PREFACE TO THE FIRST EDITION
`
`Most sound engineers will agree that the microphone is the most
`important element in any audio chain, and certainly the dazzling array
`of current models, including many that are half-a-century old, attests to
`that fact. My love affair with the microphone began when I was in my
`teens and got my hands on a home-type disc recorder. Its crystal micro-
`phone was primitive, but I was nonetheless hooked. The sound bug had
`bitten me, and, years of music schooling not withstanding, it was
`inevitable that I would one day end up a recording engineer.
`About thirty years ago I began teaching recording technology at vari-
`ous summer educational programs, notably those at the Eastman School
`of Music and later at the Aspen Music Festival and Peabody Conservatory.
`I made an effort at that time to learn the fundamentals of microphone per-
`formance and basic design parameters, and my Microphone Handbook,
`published in 1981, was a big step forward in producing a text for some of
`the earliest collegiate programs in recording technology. This new book
`from Focal Press presents the technology in greater depth and detail and,
`equally important, expands on contemporary usage and applications.
`The Microphone Book is organized so that both advanced students
`in engineering and design and young people targeting a career in audio
`can learn from it. Chapter 1 presents a short history of the microphone.
`While Chapters 2 through 6 present some mathematically intensive
`material, their clear graphics will be understandable to those with little
`technical background. Chapters 7 through 10 deal with practical matters
`such as standards, the microphone-studio electronic interface, and all
`types of accessories.
`Chapters 11 through 17 cover the major applications areas, with
`emphasis on the creative aspects of music recording in stereo and sur-
`round sound, broadcast/communications, and speech/music reinforce-
`ment. Chapter 18 presents an overview of advanced development in
`microphone arrays, and Chapter 19 presents helpful hints on microphone
`maintenance and checkout. The book ends with a comprehensive micro-
`phone bibliography and index.
`
`8
`
`

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`
`viii
`
`Preface to the First Edition
`
`I owe much to Leo Beranek’s masterful 1954 Acoustics text, A. E.
`Robertson’s little known work, Microphones, which was written for the
`BBC in 1951, as well as the American Institute of Physics’ Handbook of
`Condenser Microphones. As always, Harry Olson’s books came to my
`aid with their encyclopedic coverage of everything audio.
`Beyond these four major sources, any writer on microphones must
`rely on technical journals and on-going discussions with both users and
`manufacturers in the field. I would like to single out for special thanks
`the following persons for their extended technical dialogue: Norbert
`Sobol (AKG Acoustics), Jörg Wuttke (Schoeps GmbH), David Josephson
`(Josephson Engineering), Keishi Imanaga (Sanken Microphones), and in
`earlier days Steve Temmer and Hugh Allen of Gotham Audio. Numerous
`manufacturers have given permission for the use of photographs and
`drawings, and they are credited with each usage in the book.
`
`John Eargle
`April 2001
`
`9
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`
`PREFACE TO THE
`SECOND EDITION
`
`The second edition of The Microphone Book follows the same broad
`subject outline as the first edition. Most of the fundamental chapters
`have been updated to reflect new models and electronic technology,
`while those chapters dealing with applications have been significantly
`broadened in their coverage.
`The rapid growth of surround sound technology merits a new chap-
`ter of its own, dealing not only with traditional techniques but also with
`late developments in virtual imaging and the creation of imaging that
`conveys parallax in the holographic sense.
`Likewise, the chapter on microphone arrays has been expanded to
`include discussions of adaptive systems as they involve communications
`and useful data reduction in music applications.
`Finally, at the suggestion of many, a chapter on classic microphones
`has been included. Gathering information on nearly thirty models was a
`far more difficult task than one would ever have thought, and it was
`truly a labor of love.
`
`John Eargle
`Los Angeles, June 2004
`
`10
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`
`SYMBOLS USED IN THIS BOOK
`
`a
`A
`AF
`c
`⬚C
`d
`dB
`dB(A)
`dBu
`DC
`DI
`E
`e(t)
`f
`HF
`Hz
`I
`I
`i(t)
`I0
`j
`k
`kg
`⬚K
`LF
`LP
`LR
`LN
`m
`MF
`mm
`␮m
`
`radius of diaphragm (mm); acceleration (m/s2)
`ampere (unit of electrical current)
`audio frequency
`speed of sound (334 m/s at normal temperature)
`temperature (degrees celsius)
`distance (m)
`relative level (decibel)
`A-weighted sound pressure level
`signal voltage level (re 0.775 volt rms)
`critical distance (m)
`directivity index (dB)
`voltage (volt dc)
`signal voltage (volt rms)
`frequency in hertz (s–1)
`high frequency
`frequency (hertz, cycles per second)
`acoustical intensity (W/m2)
`dc electrical current, ampere (Q/s)
`signal current (ampere rms)
`mechanical moment of inertia (kg ⫻ m2)
`兹 ⫺ 1
`complex algebraic operator, equal to
`wave number (2␲/␭)
`mass, kilogram (SI base unit)
`temperature (degrees kelvin, SI base unit)
`low frequency
`sound pressure level (dB re 20 ␮Pa)
`reverberant sound pressure level (dB re 20 ␮Pa)
`noise sound pressure level (dB re 20 ␮Pa)
`meter (SI base unit)
`mid frequency
`millimeter (m ⫻ 10–3)
`micrometer or micron (m ⫻ 10–6)
`
`11
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`Symbols Used in This Book
`
`xi
`
`M
`MD
`N
`p; p(t)
`P
`Q
`Q
`r
`R, ⍀
`R
`RE
`RF
`RH
`s
`S
`T
`T, t
`T
`T60
`T0
`torr
`
`u; u(t)
`U, U(t)
`x(t)
`X
`V
`Z
`␣
`␭
`␾
`␳
`␳0
`␳0c
`␪
`
`␻
`␴m
`
`microphone system sensitivity, mV/Pa
`capacitor microphone base diaphragm sensitivity, V/Pa
`force, newton (kg, m/s2)
`rms sound pressure (N/m2)
`power (watt)
`electrical charge (coulombs, SI base unit)
`directivity factor
`distance from sound source (m)
`electrical resistance (ohm)
`room constant (m3 or ft3)
`random efficiency of microphone (also REE)
`radio frequency
`relative humidity (%)
`second (SI base unit)
`surface area (m2)
`torque (N ⫻ m)
`time (s)
`magnetic flux density (tesla)
`reverberation time (seconds)
`diaphragm tension (newton/meter)
`atmospheric pressure; equal to mm of mercury (mmHg), or
`133.322 Pa (Note: 760 torr is equal to normal atmospheric
`pressure at 0⬚C)
`air particle rms velocity (m/s)
`air volume rms velocity (m3/s)
`air particle displacement (m/s)
`mechanical, acoustical, or electrical reactance (⍀)
`electrical voltage (voltage or potential)
`mechanical, acoustical or electrical resistance (⍀)
`average absorption coefficient (dimensionless)
`wavelength of sound in air (m)
`phase, phase shift (degrees or radians)
`dependent variable in polar coordinates
`density of air (1.18 kg/m3)
`specific acoustical impedance of air (415 SI rayls)
`angle (degrees or radians), independent variable in polar
`coordinates
`2␲f (angular frequency in radians/s)
`surface mass density (kg/m2)
`
`12
`
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`13
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`
`C H A P
`
`T
`
`E R
`
`2
`
`BASIC SOUND
`TRANSMISSION AND
`OPERATIONAL FORCES
`ON MICROPHONES
`
`INTRODUCTION
`
`All modern microphones benefit from electrical amplification and thus
`are designed primarily to sample a sound field rather than take power
`from it. In order to understand how microphones work from the physi-
`cal and engineering points of view, we must understand the basics of
`sound transmission in air. We base our discussion on sinusoidal wave
`generation, since sine waves can be considered the building blocks of
`most audible sound phenomena. Sound transmission in both plane and
`spherical waves will be discussed, both in free and enclosed spaces.
`Power relationships and the concept of the decibel are developed. Finally,
`the effects of microphone dimensions on the behavior of sound pickup
`are discussed.
`
`BASIC WAVE GENERATION AND
`TRANSMISSION
`
`Figure 2–1 illustrates the generation of a sine wave. The vertical compo-
`nent of a rotating vector is plotted along the time axis, as shown at A.
`At each 360⬚ of rotation, the wave structure, or waveform, begins anew.
`The amplitude of the sine wave reaches a crest, or maximum value,
`above the zero reference baseline, and the period is the time required for
`the execution of one cycle. The term frequency represents the number of
`cycles executed in a given period of time. Normally we speak of fre-
`quency in hertz (Hz), representing cycles per second.
`
`14
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`

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`
`8
`
`THE MICROPHONE BOOK
`
`FIGURE 2–1
`
`Generation of a sine
`wave signal (A); phase
`relationships between two
`sine waves (B).
`
`For sine waves radiating outward in a physical medium such as air,
`the baseline in Figure 2–1 represents the static atmospheric pressure,
`and the sound waves are represented by the alternating plus and minus
`values of pressure about the static pressure. The period then corresponds
`to wavelength, the distance between successive iterations of the basic
`waveform.
`The speed of sound transmission in air is approximately equal to
`344 meters per second (m/s), and the relations among speed (m/s), wave-
`length (m), and frequency (1/s) are:
`
`c (speed) ⫽ f (frequency) ⫻ ␭ (wavelength)
`f ⫽ c/␭
`␭ ⫽ c/f
`
`(2.1)
`
`For example, at a frequency of 1000 Hz, the wavelength of sound in air
`will be 344/1000 ⫽ 0.344 m (about 13 inches).
`Another fundamental relationship between two waveforms of the
`same frequency is their relative phase (␾), the shift of one period relative
`to another along the time axis as shown in Figure 2–1B. Phase is nor-
`mally measured in degrees of rotation (or in radians in certain mathe-
`matical operations). If two sound waves of the same amplitude and
`
`15
`
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`
`2: Basic Sound Transmission and Operational Forces on Microphones
`
`9
`
`FIGURE 2–2
`
`Wavelength of sound in air
`versus frequency; in meters
`(A); in feet (B).
`
`frequency are shifted by 180⬚ they will cancel, since they will be in an
`inverse (or anti-phase) relationship relative to the zero baseline at all
`times. If they are of different amplitudes, then their combination will not
`directly cancel.
`The data shown in Figure 2–2 gives the value of wavelength in air
`when frequency is known. (By way of terminology, velocity and speed
`are often used interchangeably. In this book, speed will refer to the rate
`of sound propagation over distance, while velocity will refer to the
`specifics of localized air particle and air volume movement.)
`
`TEMPERATURE DEPENDENCE OF SPEED OF
`SOUND TRANSMISSION
`
`For most recording activities indoors, we can assume that normal tem-
`peratures prevail and that the effective speed of sound propagation will
`be as given above. There is a relatively small dependence of sound prop-
`agation on temperature, as given by the following equation:
`Speed ⫽ 331.4 ⫹ 0.607 ⬚C m/s
`where ⬚C is the temperature in degrees celsius.
`
`(2.2)
`
`16
`
`

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`10
`
`THE MICROPHONE BOOK
`
`ACOUSTICAL POWER
`
`In any kind of physical system in which work is done, there are two
`quantities, one intensive, the other extensive, whose product determines
`the power, or rate at which work is done in the system. One may intu-
`itively think of the intensive variable as the driving agent and the exten-
`sive variable as the driven agent. Table 2–1 may make this clearer.
`Power is stated in watts (W), or joules/second. The joule is the unit
`of work or energy, and joules per second is the rate at which work is
`done, or energy expended. This similarity among systems makes it easy
`to transform power from one physical domain to another, as we will see
`in later chapters.
`Intensity (I) is defined as power per unit area (W/m2), or the rate of
`energy flow per unit area. Figure 2–3 shows a sound source at the left
`radiating an acoustical signal of intensity I0 uniformly into free space.
`We will examine only a small solid angle of radiation. At a distance of
`10 m that small solid angle is radiating through a square with an area of
`1 m2, and only a small portion of I0 will pass through that area. At a dis-
`tance of 20 m the area of the square that accommodates the original solid
`angle is now 4 m2, and it is now clear that the intensity at a distance of
`20 m will be one-fourth what it was at 10 m. This of course is a neces-
`sary consequence of the law of conservation of energy.
`
`TABLE 2–1 Intensive and extensive variables
`
`System
`
`Intensive variable
`
`Extensive variable
`
`Product
`
`Electrical
`Mechanical
`(rectilinear)
`Mechanical
`(rotational)
`Acoustical
`
`voltage (e)
`force (f )
`
`torque (T)
`
`current (i)
`velocity (u)
`
`watts (e ⫻ i)
`watts (f ⫻ u)
`
`angular velocity (␪)
`
`watts (T ⫻ ␪)
`
`pressure (p)
`
`volume velocity (U)
`
`watts (p ⫻ U)
`
`FIGURE 2–3
`
`Sound intensity variation
`with distance over a fixed
`solid angle.
`
`17
`
`

`

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`
`2: Basic Sound Transmission and Operational Forces on Microphones
`
`11
`
`The relationship of intensity and distance in a free sound field is
`know as the inverse square law: as intensity is measured between dis-
`tances of r and 2r, the intensity changes from 1/I0 to 1/4I0.
`The intensity at any distance r from the source is given by:
`I ⫽ W/4␲r2
`
`(2.3)
`
`The effective sound pressure in pascals at that distance will be:
`p ⫽ 兹I␳0c
`where ␳0c is the specific acoustical impedance of air (405 SI rayls).
`For example, consider a point source of sound radiating a power of
`one watt uniformly. At a distance of 1 meter the intensity will be:
`I ⫽ 1/4␲(1)2 ⫽ 1/4␲ ⫽0.08 W/m 2
`
`(2.4)
`
`The effective sound pressure at that distance will be:
`p ⫽ 兹(0.08)405 ⫽ 5.69 Pa
`
`RELATIONSHIP BETWEEN AIR PARTICLE
`VELOCITY AND AMPLITUDE
`
`The relation between air particle velocity (u) and particle displacement
`(x) is given by:
`
`u(t) ⫽ j␻ ⫻(t)
`(2.5)
`where ␻ ⫽2␲f and x(t) is the maximum particle displacement value. The
`complex operator j produces a positive phase shift of 90⬚.
`Some microphones, notably those operating on the capacitive or
`piezoelectric principle, will produce constant output when placed in a
`constant amplitude sound field. In this case u(t) will vary proportional to
`frequency.
`Other microphones, notably those operating on the magnetic induc-
`tion principle, will produce a constant output when placed in a constant
`velocity sound field. In this case, x(t) will vary inversely proportional to
`frequency.
`
`THE DECIBEL
`
`We do not normally measure acoustical intensity; rather, we measure
`sound pressure level. One cycle of a varying sinusoidal pressure might look
`like that shown in Figure 2–4A. The peak value of this signal is shown as
`unity; the root-mean-square value (rms) is shown as 0.707, and the aver-
`age value of the waveform is shown as 0.637. A square wave of unity
`value, shown at B, has peak, rms, and average values that all are unity. The
`rms, or effective, value of a pressure waveform corresponds directly to the
`power that is delivered or expended in a given acoustical system.
`The unit of pressure is the pascal (Pa) and is equal to one newton/m2.
`(The newton (N) is a unit of force that one very rarely comes across in
`
`18
`
`

`

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`
`12
`
`THE MICROPHONE BOOK
`
`FIGURE 2–4
`
`Sine (A) and square (B)
`waves: definitions of peak,
`rms and average values.
`
`daily life and is equal to about 9.8 pounds of force.) Pressures encoun-
`tered in acoustics normally vary from a low value of 20 ␮Pa (micropas-
`cals) up to normal maximum values in the range of 100 Pa. There is a
`great inconvenience in dealing directly with such a large range of num-
`bers, and years ago the decibel (dB) scale was devised to simplify things.
`The dB was originally intended to provide a convenient scale for looking
`at a wide range of power values. As such, it is defined as:
`Level (dB) ⫽ 10 log (W/W0)
`(2.6)
`where W0 represents a reference power, say, 1 watt, and the logarithm is
`taken to the base 10. (The term level is universally applied to values
`expressed in decibels.) With one watt as a reference, we can say that
`20 watts represents a level of 13 dB:
`Level (dB) ⫽ 10 log (20/1) ⫽ 13 dB
`
`Likewise, the level in dB of a 1 milliwatt signal, relative to one watt, is:
`Level (dB) ⫽ 10 log (0.001/1) ⫽ ⫺30 dB
`
`From basic electrical relationships, we know that power is propor-
`tional to the square of voltage. As an analog to this, we can infer that
`acoustical power is proportional to the square of acoustical pressure. We
`can therefore rewrite the definition of the decibel in acoustics as:
`Level (dB) ⫽ 10 log (p/p0)2 ⫽ 20 log (p/p0)
`(2.7)
`In sound pressure level calculations, the reference value, or p0, is estab-
`lished as 0.00002 Pa, or 20 micropascals (20 ␮Pa).
`Consider a sound pressure of one Pa. Its level in dB is:
`dB ⫽ 20 log (1/0.00002) ⫽ 94 dB
`
`This is an important relationship. Throughout this book, the value of 94
`dB LP will appear time and again as a standard reference level in micro-
`phone design and specification. (LP is the standard terminology for sound
`pressure level.)
`Figure 2–5 presents a comparison of a number of acoustical sources
`and the respective levels at reference distances.
`
`19
`
`

`

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`
`2: Basic Sound Transmission and Operational Forces on Microphones
`
`13
`
`FIGURE 2–5
`
`Sound pressure levels of
`various sound sources.
`
`The graph in Figure 2–6 shows the relationship between pressure in
`Pa and LP. The nomograph shown in Figure 2–7 shows the loss in dB
`between any two reference distances from a point source in the free field.
`Referring once again to equation (2.4), we will now calculate the
`sound pressure level of one acoustical watt measured at a distance of 1 m
`from a spherically radiating source:
`LP ⫽ 20 log (5.69/0.00002) ⫽ 109 dB
`It can be appreciated that one acoustical watt produces a consider-
`able sound pressure level. From the nomograph of Figure 2–7, we can
`see that one acoustical watt, radiated uniformly and measured at a
`
`20
`
`

`

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`
`14
`
`THE MICROPHONE BOOK
`
`FIGURE 2–6
`
`Relationship between
`sound pressure and sound
`pressure level.
`
`FIGURE 2–7
`
`Inverse square sound pressure level relationships as a function of distance from the source; to determine the level difference
`between sound pressures at two distances, located the two distances and then read the dB difference between them; for
`example, determine the level difference between distances 50 m and 125 m from a sound source; above 50 read a level of
`34 dB; above 125 read a level of 42 dB; taking the difference gives 8 dB.
`
`distance of 10 m (33 feet), will produce LP ⫽ 89 dB. How “loud” is a
`signal of 89 dB LP? It is approximately the level of someone shouting in
`your face!
`
`THE REVERBERANT FIELD
`
`A free field exists only under specific test conditions. Outdoor conditions
`may approximate it. Indoors, we normally observe the interaction of a
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`15
`
`direct field and a reverberant field as we move away from a sound
`source. This is shown pictorially in Figure 2–8A. The reverberant field
`consists of the ensemble of reflections in the enclosed space, and rever-
`beration time is considered to be that time required for the reverberant
`field to diminish 60 dB after the direct sound source has stopped.
`There are a number of ways of defining this, but the simplest is given
`by the following equation:
`
`Reverberation time (s) ⫽
`
`0.16 V
`S ␣
`
`(2.8)
`
`where V is the room volume in m3, S is the interior surface area in m2,
`␣
`and
`is the average absorption coefficient of the boundary surfaces.
`The distance from a sound source to a point in the space where both
`direct and reverberant fields are equal is called critical distance (DC).
`In live spaces critical distance is given by the following equation:
`
`FIGURE 2–8
`
`The reverberant field.
`Illustration of reflections
`in an enclosed space
`compared to direct sound
`at a variable distance from
`the sound source (A);
`interaction of direct and
`reverberant fields in a live
`space (B); interaction of
`direct and reverberant
`fields in a damped
`space (C).
`
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`THE MICROPHONE BOOK
`
`(2.9)
`
`DC ⫽ 0.14兹QS␣
`where Q is the directivity factor of the source. We will discuss this topic
`in further detail in Chapter 17.
`␣
`In a live acoustical space, may be in the range of 0.2, indicating
`that, on average, only 20% of the incident sound power striking the
`boundaries of the room will be absorbed; the remaining 80% will reflect
`from those surfaces, strike other surfaces, and be reflected again. The
`process will continue until the sound is effectively damped out.
`Figures 2–8B and C show, respectively, the observed effect on sound
`pressure level caused by the interaction of direct, reflected, and reverber-
`ant fields in live and damped spaces.
`Normally, microphones are used in the direct field or in the transi-
`tion region between direct and reverberant fields. In some classical
`recording operations, a pair of microphones may be located well within
`the reverberant field and subtly added to the main microphone array for
`increased ambience.
`
`SOUND IN A PLANE WAVE FIELD
`
`For wave motion in a free plane wave field, time varying values of sound
`pressure will be in phase with the air particle velocity, as shown in
`Figure 2–9. This satisfies the conditions described in Table 2.1, in which
`the product of pressure and air volume velocity define acoustical power.
`(Volume velocity may be defined here as the product of particle velocity
`and the area over which that particle velocity is observed.)
`If a microphone is designed to respond to sound pressure, the con-
`ditions shown in Figure 2–9A are sufficient to ensure accurate reading of
`the acoustical sound field.
`Most directional microphones are designed to be sensitive to the air
`pressure difference, or gradient, existing between two points along a
`given pickup axis separated by some distance l. It is in fact this sensitiv-
`ity that enables these microphones to produce their directional pickup
`characteristics. Figure 2–9B shows the phase relationships at work here.
`The pressure gradient [dp/dl] is in phase with the particle displacement
`[x(t)]. However, the particle displacement and particle velocity [dx/dt]
`are at a 90⬚ phase relationship.
`These concepts will become clearer in later chapters in which we
`discuss the specific pickup patterns of directional microphones.
`
`SOUND IN A SPHERICAL WAVE FIELD
`
`Relatively close to a radiating sound source, the waves will be more or
`less spherical. This is especially true at low frequencies, where the differ-
`ence in wavefront curvature for successive wave crests will be quite
`pronounced. As our observation point approaches the source, the phase
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`
`FIGURE 2–9
`
`Wave considerations
`in microphone
`performance: relationship
`between sound pressure
`and particle velocity (A);
`relationship among air
`particle velocity, air particle
`displacement, and pressure
`gradient (B); relationship
`between pressure and
`pressure gradient (C) (Data
`presentation after
`Robertson, 1963).
`
`angle between pressure and particle velocity will gradually shift from zero
`(in the far field) to 90⬚, as shown in Figure 2–10A. This will cause an
`increase in particle velocity with increasing phase shift, as shown at B.
`As we will see in a later detailed discussion of pressure gradient
`microphones, this phenomenon is responsible for what is called proxim-
`ity effect, the tendency of directional microphones to increase their LF
`(low frequency) output at close operating distances.
`
`EFFECTS OF HUMIDITY ON SOUND TRANSMISSION
`
`Figure 2–11 shows the effects of both inverse square losses and HF losses
`due to air absorption. Values of relative humidity (RH) of 20% and 80%
`are shown here. Typical losses for 50% RH would be roughly halfway
`between the plotted values shown.
`For most studio recording operations HF losses may be ignored.
`However, if an organ recording were to be made at a distance of 12 m in
`a large space and under very dry atmospheric conditions, the HF losses
`could be significant, requiring an additional HF boost during the record-
`ing process.
`
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`THE MICROPHONE BOOK
`
`FIGURE 2–10
`
`Spherical sound waves:
`phase angle between
`pressure and particle
`velocity in a spherical
`wave at low frequencies; r
`is the observation distance
`and ␭ is the wavelength of
`the signal (A); increase in
`pressure gradient in a
`spherical wave at low
`frequencies (B).
`
`FIGURE 2–11
`
`Effects of both inverse
`square relationships and
`HF air losses (20% and
`80% RH).
`
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`19
`
`DIFFRACTION EFFECTS AT SHORT WAVELENGTHS;
`DIRECTIVITY INDEX (DI)
`
`Microphones are normally fairly small so that they will have minimal effect
`on the sound field they are sampling. There is a limit, however, and it is dif-
`ficult to manufacture studio quality microphones smaller than about 12 mm
`(0.5 in) in diameter. As microphones operate at higher frequencies, there are
`bound to be certain aberrations in directional response as the dimensions of
`the microphone case become a significant portion of the sound wavelength.
`Diffraction refers to the bending of sound waves as they encounter objects
`whose dimensions are a significant portion of a wavelength.
`Many measurements of off-axis microphone response have been
`made over the years, and even more theoretical graphs have been devel-
`oped. We will now present some of these.
`
`FIGURE 2–12
`
`Theoretical polar
`response for a microphone
`mounted at the end of a
`tube. (Data presentation
`after Beranek, 1954.)
`
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`THE MICROPHONE BOOK
`
`Figure 2–12 shows polar response diagrams for a circular diaphragm
`at the end of a long tube, a condition that describes many microphones. In
`the diagrams, ka ⫽ 2␲a/␭, where a is the radius of the diaphragm. Thus,
`ka represents the diaphragm circumference divided by wavelength. DI
`stands for directivity index; it is a value, expressed in decibels, indicating
`the ratio of on-axis pickup relative to the total pickup integrated over all
`directions. Figure 2–13 shows the same set of measurements for a micro-
`phone which is effectively open to the air equally on both sides. It repre-
`sents the action a ribbon microphone, with its characteristic “figure-eight”
`angular response.
`Figure 2–14 shows families of on- and off-axis frequency response
`curves for microphones mounted on the indicated surfaces of a cylinder
`and a sphere. Normally, a limit for the HF response of a microphone
`would be a diameter/␭ ratio of about one.
`In addition to diffraction effects, there are related response aberra-
`tions due to the angle at which sound impinges on the microphone’s
`diaphragm. Figure 2–15A shows a plane wave impinging at an off-axis
`oblique angle on a microphone diaphragm subtended diameter which is
`one-fourth of the sound wavelength. It can be seen that the center por-
`tion of the diaphragm is sampling the full value of the waveform, while
`adjacent portions are sampling a slightly lesser value. Essentially, the
`diaphragm will respond accurately, but with some small diminution of
`output for the off-axis pickup angle shown here.
`
`FIGURE 2–13
`
`Theoretical polar response
`for a free microphone
`diaphragm open on both
`sides. (Data presentation
`after Beranek, 1954.)
`
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`21
`
`FIGURE 2–14
`
`On and off-axis frequency
`response for microphones
`mounted on the end of a
`cylinder and a sphere. (Data
`after Muller et al., 1938.)
`
`FIGURE 2–15
`
`Plane sound waves
`impinging on a microphone
`diaphragm at an oblique
`angle. Microphone
`diaphragm subtended
`diameter equal to ␭/4 (A);
`microphone diaphragm
`subtended diameter equal
`to ␭ (B). (Data after
`Robertson, 1963.)
`
`The condition shown in Figure 2–15B is for an off-axis sound wave-
`length which is equal to the subtended diameter of the microphone
`diaphragm. Here, the diaphragm samples the entire wavelength, which
`will result in near cancellation in response over the face of the
`diaphragm.
`
`28
`
`