everest f.a. the master handbook of acoustics

the Ear 72Perception of Reflected Sound 75Occupational and Recreational Deafness 76Summary 79 Chapter 4 Sound Waves in the Free Field 83 Free Sound Field: Definition 83 Examples: Free-fi

OF ACOUSTICS

OF ACOUSTICS

F Alton Everest FOURTH EDITION

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what-DOI: 10.1036/0071399747

Epigraph xxi

Wavelength and Frequency 10

Electrical, Mechanical, and Acoustical Analogs 20

Ratios vs Differences 23

Logarithms 26Decibels 26

Using Decibels 33

Example: Microphone specifications 35

Example: General-purpose amplifier 35

Measuring Sound-Pressure Level 39

Chapter 3 The Ear and the Perception of Sound 41

Sensitivity of the Ear 41

A Primer of Ear Anatomy 42

The pinna: Directional encoder of sound 43

Directional cues: An experiment 44

Aural harmonics: Experiment #1 68

Aural harmonics: Experiment #2 69

The Ear as an Analyzer 70The Ear as a Measuring Instrument 70

An auditory analyzer: An experiment 71

Meters vs the Ear 72

Perception of Reflected Sound 75Occupational and Recreational Deafness 76Summary 79

Chapter 4 Sound Waves in the Free Field 83

Free Sound Field: Definition 83

Examples: Free-field sound divergence 84

Inverse square in enclosed spaces 87

Chapter 6 Analog and Digital Signal Processing 119

Resonance 120Filters 122

Mode Decay Variations 142

Reverberation Time Variation with Position 145Acoustically Coupled Spaces 146Electroacoustically Coupled Spaces 146

Eliminating decay fluctuations 147Influence of Reverberation on Speech 148Influence of Reverberation on Music 149Optimum Reverberation Time 150

Bass rise of reverberation time 152

Living room reverberation time 154

Artificial Reverberation: The Past 155Artificial Reverberation: The Future 156

Reverberation calculation: Example 1 160

Reverberation calculation: Example 2 162

Chapter 8 Control of Interfering Noise 165

Noise Sources and Some Solutions 166

Noise transmitted by diaphragm action 168

Dissipation of Sound Energy 179Evaluation of Sound Absorption 181Reverberation Chamber Method 182Impedance Tube Method 182

Mounting of Absorbents 186Mid/High Frequency Absorption by Porosity 187

Glass fiber: Building insulation 189

Effect of Thickness of Absorbent 190Effect of Airspace behind Absorbent 191Effect of Density of Absorbent 192

Open-Cell Foams 192Drapes as Sound Absorbers 193Carpet as Sound Absorber 196

Effect of carpet type on absorbance 199

Effect of carpet underlay on absorbance 200

Carpet absorption coefficients 200Sound Absorption by People 200Absorption of Sound in Air 203Low-Frequency Absorption by Resonance 203Diaphragmatic Absorbers 205Polycylindrical Absorbers 209

Increasing Reverberation Time 229Modules 229

Reflections from Flat Surfaces 235Doubling of Pressure at Reflection 237Reflections from Convex Surfaces 237Reflections from Concave Surfaces 237Reflections from Parabolic Surfaces 238Reflections inside a Cylinder 240

Chapter 11 Diffraction of Sound 245

Rectilinear Propagation 245Diffraction and Wavelength 246Diffraction of Sound by Large and Small Apertures 247Diffraction of Sound by Obstacles 248Diffraction of Sound by a Slit 249Diffraction by the Zone Plate 250Diffraction around the Human Head 251Diffraction by Loudspeaker Cabinet Edges 253Diffraction by Various Objects 254

Refraction of sound in solids 258

Refraction of sound in the atmosphere 260

Refraction of sound in the ocean 263

Refraction of sound in enclosed spaces 265

The Perfectly Diffuse Sound Field 267Evaluating Diffusion in a Room 268

Chapter 14 The Schroeder Diffusor 289

Schroeder’s First Acoustic Diffusor 290Maximum-Length Sequences 292Reflection Phase-Grating Diffusors 292Quadratic-Residue Diffusors 293Primitive-Root Diffusors 296Quadratic-Residue Applications 298Performance of Diffraction-Grating Diffusors 298

Diffusion in three dimensions 308

Measuring diffusion efficiency 311Comparison of Gratings with Conventional

The Bonello Criterion 348Controlling Problem Modes 348

Chapter 16 Reflections in Enclosed Spaces 353

Law of the First Wavefront 353

The effect of single reflections 355

Perception of sound reflections 355

Effect of signal type of audibility of reflection 358

Effect of spectrum on audibility of reflection 358

Spaciousness 360

What Is a Comb Filter? 363Superposition of Sound 364Tonal Signals and Comb Filters 365

Combing of music and speech signals 367

Combing of direct and reflected sound 368Comb Filters and Critical Bands 371Comb Filters in Stereo Listening 374Coloration and Spaciousness 374Combing in Stereo Microphone Pickups 375Audibility of Comb-Filter Effects 375

Estimating comb-filter response 380

Selection of Noise Criterion 386

Some Practical Suggestions 395

Chapter 19 Acoustics of the Listening Room 399

Peculiarities of Small-Room Acoustics 400

The Listening Room: Low Frequencies 403

Bass traps for the listening room 406

The Listening Room: The Mid-High Frequencies 409

Identification and treatment of

Lateral reflections: Control of spaciousness 413

Chapter 20 Acoustics of the Small Recording Studio 415

Acoustical Characteristics of a Studio 416Reverberation 418

Diffusion 423Noise 424Studio Design Procedure 424

Elements Common to all Studios 427

Chapter 21 Acoustics of the Control Room 429

The Initial Time-Delay Gap 429

Specular Reflections vs Diffusion 432Low-Frequency Resonances in the Control Room 434Initial Time-Delay Gaps in Practice 436

The Reflection-Free-Zone Control Room 439Control-Room Frequency Range 441Outer Shell of the Control Room 442Inner Shell of the Control Room 442Representative Control Rooms 442Some European Designs 444Consultants 450

Chapter 22 Acoustics for Multitrack Recording 453

Flexibility 545Advantages of Multitrack 455Disadvantages of Multitrack 456Achieving Track Separation 457

Chapter 23 Audio/Video Tech Room and Voice-Over

Recording 461

Selection of Space: External Factors 462Selection of Space: Internal Factors 462

Audio/Video Work Place Example 463Appraisal of Room Resonances 463

Calculations 465

Dead-End Live-End Voice Studio 468

The Quick Sound Field™ 469

Draperies 473Adjustable Panels: Absorption 474Adjustable Panels: The Abffusor™ 476

Acoustic Distortion and the Perception of Sound 489Sources of Acoustic Distortion 490

Speaker-boundary interference response 491

Conclusion 500

Chapter 26 Room Acoustics Measurement Software 501

The Evolution of Measurement Technologies 502

Building a Better Analyzer 504

Time-delay spectrometry (TDS) measurement

Optimization Procedure 545Results 549

Appendix 585 Glossary 589

Directly or indirectly, all questions connected with this subject must

come for decision to the ear, as the organ of hearing; and from it there

can be no appeal But we are not therefore to infer that all acoustical

investigations are conducted with the unassisted ear When once we

have discovered the physical phenomena which constitute the

founda-tion of sound, our explorafounda-tions are in great measure transferred to

another field lying within the dominion of the principles of Mechanics.

Important laws are in this way arrived at, to which the sensations of

the ear cannot but conform.

Lord Raleigh in The Theory of Sound,

Excerpts from the introduction to the third edition.

In 1981, the copyright year of the first edition of this book, Manfred

Schroeder was publishing his early ideas on applying number theory

to the diffusion of sound In the third edition a new chapter has been

added to cover numerous applications of diffraction-grating diffusors

to auditoriums, control rooms, studios and home listening rooms

Introduction to the fourth edition.

The science of acoustics made great strides in the 20th century, during

which the first three editions of this book appeared This fourth

edi-tion, however, points the reader to new horizons of the 21st century A

newly appreciated concept of distortion of sound in the medium itself

(Chap 25), a program for acoustic measurements (Chap 26), and the

optimization of placement of loudspeakers and listener (Chap 27), all

based on the home computer, point forward to amazing developments

in acoustics yet to come

As in the previous three editions, this fourth edition balances

treat-ment of the fundatreat-mentals of acoustics with the general application of

fundamentals to practical problems

F Alton Everest

Santa Barbara

Copyright 2001 The McGraw-Hill Companies, Inc Click Here for Terms of Use

Sound can be defined as a wave motion in air or other elastic

media (stimulus) or as that excitation of the hearing mechanism

that results in the perception of sound (sensation) Which definition

applies depends on whether the approach is physical or

psy-chophysical The type of problem dictates the approach to sound If

the interest is in the disturbance in air created by a loudspeaker, it is

a problem in physics If the interest is how it sounds to a person near

the loudspeaker, psychophysical methods must be used Because

this book addresses acoustics in relation to people, both aspects of

sound will be treated

These two views of sound are presented in terms familiar to those

interested in audio and music Frequency is a characteristic of

peri-odic waves measured in hertz (cycles per second), readily observable

on a cathode-ray oscilloscope or countable by a frequency counter

The ear perceives a different pitch for a soft 100 Hz tone than a loud

one The pitch of a low-frequency tone goes down, while the pitch of

a high-frequency tone goes up as intensity increases A famous

acoustician, Harvey Fletcher, found that playing pure tones of 168 and

318 Hz at a modest level produces a very discordant sound At a high

intensity, however, the ear hears the pure tones in the 150-300 Hz

octave relationship as a pleasant sound We cannot equate frequency

and pitch, but they are analogous

The same situation exists between intensity and loudness The

rela-tionship between the two is not linear This is considered later in moredetail because it is of great importance in high fidelity work

Similarly, the relationship between waveform (or spectrum) and perceived quality (or timbre) is complicated by the functioning of the

hearing mechanism As a complex waveform can be described interms of a fundamental and a train of harmonics (or partials) of variousamplitudes and phases (more on this later), the frequency-pitch inter-action is involved as well as other factors

The Simple Sinusoid

The sine wave is a basic waveform closely

related to simple harmonic motion Theweight (mass) on the spring shown in Fig 1-1 is a vibrating system If the weight ispulled down to the 5 mark and released,the spring pulls the weight back toward 0.The weight will not, however, stop at zero; itsinertia will carry it beyond 0 almost to 5.The weight will continue to vibrate, or oscil-late, at an amplitude that will slowlydecrease due to frictional losses in the spring,the air, etc

The weight in Fig 1-1 moves in what iscalled simple harmonic motion The pis-ton in an automobile engine is connected to the crankshaft by a con-necting rod The rotation of the crankshaft and the up-and-downmotion of the pistons beautifully illustrate the relationship betweenrotary motion and linear simple harmonic motion The piston positionplotted against time produces a sine wave It is a very basic type ofmechanical motion, and it yields an equally basic waveshape in soundand electronics

If a ballpoint pen is fastened to the pointer of Fig 1-2, and a strip ofpaper is moved past it at a uniform speed, the resulting trace is a sinewave

In the arrangement of Fig 1-1, vibration or oscillation is possible

because of the elasticity of the spring and the inertia of the weight.

A weight on a spring vibrates at its natural frequency

because of the elasticity of the spring and the

iner-tia of the weight.

Elasticity and inertia are two things all media must possess to be

capa-ble of conducting sound

Sine-Wave Language

The sine wave is a specific kind of alternating signal and is described

by its own set of specific terms Viewed on an oscilloscope, the easiest

value to read is the peak-to-peak value (of voltage, current, sound

pressure, or whatever the sine wave represents), the meaning of which

is obvious in Fig 1-3 If the wave is symmetrical, the peak-to-peak

value is twice the peak value

The common ac voltmeter is, in reality, a dc instrument fitted with

a rectifier that changes the alternating sine current to pulsating

unidi-rectional current The dc meter then responds to the average value as

indicated in Fig 1-3 Such meters are, however, almost universely

cal-ibrated in terms of rms (described in the next paragraph) For pure sine

waves, this is quite an acceptable fiction, but for nonsinusoidal

wave-shapes the reading will be in error

An alternating current of one ampere rms (or effective) is exactly

equivalent in heating power to 1 ampere of direct current as it flows

through a resistance of known value After all, alternating current can

heat up a resistor or do work no matter which direction it flows, it is

just a matter of evaluating it In the right-hand positive loop of Fig 1-3

the ordinates (height of lines to the curve) are read off for each marked

W

Paper motion

Time

F I G U R E 1 - 2

A ballpoint pen fastened to the vibrating weight traces a sine wave on a paper strip

moving at uniform speed This shows the basic relationship between simple harmonic

motion and the sine wave.

increment of time Then (a) each of these ordinate values is squared, (b)the squared values are added together, (c) the average is found, and (d)the square root is taken of the average (or mean) Taking the square root

of this average gives the root-mean-square or rms value of the positiveloop of Fig 1-3 The same can be done for the negative loop (squaring anegative ordinate gives a positive value), but simply doubling the pos-itive loop of a symmetrical wave is easier In this way the root-mean-square or “heating power” value of any alternating or periodic wavescan be determined whether the wave is for voltage, current, or soundpressure Such computations will help you understand the meaning ofrms, but fortunately reading meters is far easier Figure 1-3 is a usefulsummary of relationships pertaining only to the sine wave

Peak to peak

Propagation of Sound

If an air particle is displaced from its original position, elastic forces of

the air tend to restore it to its original position Because of the inertia

of the particle, it overshoots the resting position, bringing into play

elastic forces in the opposite direction, and so on

Sound is readily conducted in gases, liquids, and solids such as air,

water, steel, concrete, etc., which are all elastic media As a child,

per-haps you heard two sounds of a rock striking a railroad rail in the

dis-tance, one sound coming through the air and one through the rail The

sound through the rail arrives first because the speed of sound in the

dense steel is greater than that of tenuous air Sound has been detected

after it has traveled thousands of miles through the ocean

Without a medium, sound cannot be propagated In the laboratory,

an electric buzzer is suspended in a heavy glass bell jar As the button is

pushed, the sound of the buzzer is readily heard through the glass As

the air is pumped out of the bell jar, the sound becomes fainter and

fainter until it is no longer audible The sound-conducting medium, air,

has been removed between the source and the ear Because air is such a

common agent for the conduction of sound, it is easy to forget that other

gases as well as solids and liquids are also conductors of sound Outer

space is an almost perfect vacuum; no sound can be conducted except

in the tiny island of air (oxygen) within a spaceship or a spacesuit

The Dance of the Particles

Waves created by the wind travel across a field of grain, yet the

indi-vidual stalks remain firmly rooted as the wave travels on In a similar

manner, particles of air propagating a sound wave do not move far from

their undisplaced positions as shown in Fig 1-4 The disturbance

trav-els on, but the propagating particles do their little dance close to home

There are three distinct forms of particle motion If a stone is

dropped on a calm water surface, concentric waves travel out from the

point of impact, and the water particles trace circular orbits (for deep

water, at least) as in Fig 1-5(A) Another type of wave motion is

illus-trated by a violin string, Fig 1-5(B) The tiny elements of the string

move transversely, or at right angles to the direction of travel of the

waves along the string For sound traveling in a gaseous medium such

as air, the particles move in the direction the sound is traveling These

are called longitudinal waves, Fig 1-5C.

Vibration of air particle Equilibrium position

Maximum displacement

Maximum displacement

pass-A

Particle motion

Direction of wave travel

Water surface

How a Sound Wave Is Propagated

How are air particles jiggling back and forth able to carry beautiful

music from the loudspeaker to our ears at the speed of a rifle bullet?

The little dots of Fig 1-6 represent air molecules There are more than

a million molecules in a cubic inch of air; hence this sketch is greatly

exaggerated The molecules crowded together represent areas of

com-pression in which the air pressure is slightly greater than the

prevail-ing atmospheric pressure The sparse areas represent rarefactions in

which the pressure is slightly less than atmospheric The small arrows

indicate that, on the average, the molecules are moving to the right of

the compression crests and to the left in the rarefaction troughs

between the crests Any given molecule will move a certain distance to

the right and then the same distance to the left of its undisplaced

posi-tion as the sound wave progresses uniformly to the right

C

A

B

C  Compression (region of high pressure)

R  Rarefaction (region of low pressure)

Direction of sound wave

F I G U R E 1 - 6

In (A) the wave causes the air particles to be pressed together in some regions and

spread out in others An instant later (B) the wave has moved slightly to the right.

Why does the sound wave move to the right? The answer isrevealed by a closer look at the arrows of Fig 1-6 The moleculestend to bunch up where two arrows are pointing toward each other,and this occurs a bit to the right of each compression When thearrows point away from each other the density of molecules willdecrease Thus, the movement of the higher pressure crest and thelower pressure trough accounts for the small progression of thewave to the right.

As mentioned previously, the pressure at the crests is higher thanthe prevailing atmospheric barometric pressure and the troughslower than the atmospheric pressure, as shown in the sine wave ofFig 1-7 These fluctuations of pressure are very small indeed Thefaintest sound the ear can hear (20 Pascal) is some 5,000 milliontimes smaller than atmospheric pressure Normal speech and musicsignals are represented by correspondingly small ripples superim-posed on the atmospheric pressure

A

Compression

B

Rarefaction Atmospheric

Sound in Free Space

The intensity of sound decreases as the distance to the source is

increased In free space, far from the influence of surrounding objects,

sound from a point source is propagated uniformly in all directions

The intensity of sound decreases as shown in Fig 1-8 The same sound

power flows out through A1, A2, A3, and A4, but the areas increase as

the square of the radius, r This means that the sound power per unit

area (intensity) decreases as the square of the radius Doubling the

dis-tance reduces the intensity to one-fourth the initial value, tripling the

distance yields 19, and increasing the distance four times yields 116of

3r

4r

F I G U R E 1 - 8

In the solid angle shown, the same sound energy is distributed over spherical surfaces

of increasing area as r is increased The intensity of the sound is inversely proportional

to the square of the distance from the point source.

the initial intensity The inverse square law states that the intensity of

sound in a free field is inversely proportional to the square of the tance from the source This law provides the basis of estimating the

dis-sound level in many practical circumstances and is discussed in alater chapter

Wavelength and Frequency

A simple sine wave is illustrated in Fig 1-9 The wavelength is the

dis-tance a wave travels in the time it takes to complete one cycle A length can be measured between successive peaks or between any twocorresponding points on the cycle This holds for periodic waves other

wave-than the sine wave as well The frequency is the number of cycles per

second (or hertz) Frequency and wavelength are related as follows:

Wavelength

Time

Peak Amplitude

F I G U R E 1 - 9

Wavelength  (1-3)

This relationship is used frequently in following sections Figure

1-10 gives two graphical approaches for an easy solution to Equation 1-3

1,130



Frequency

(A) Convenient scales for rough determination of wavelength of sound in air from

known frequency, or vice versa (B) A chart for easy determination of the wavelength in

air of sound waves of different frequencies (Both based on speed of sound of 1,139 ft

Feet

A

Frequency - Hz 100

Complex Waves

Speech and music waveshapes depart radically from the simple sineform A very interesting fact, however, is that no matter how complex thewave, as long as it is periodic, it can be reduced to sine components Theobverse of this is that, theoretically, any complex periodic wave can besynthesized from sine waves of different frequencies, different ampli-tudes, and different time relationships (phase) A friend of Napoleon,named Joseph Fourier, was the first to develop this surprising idea Thisidea can be viewed as either a simplification or complication of the situ-ation Certainly it is a great simplification in regard to concept, but some-times complex in its application to specific speech or musical sounds

As we are interested primarily in the basic concept, let us see how even

a very complex wave can be reduced to simple sinusoidal components

the amplitude of A and three times its frequency (f3) is shown Adding

this to the f1 f2wave of C, Fig 1-11E is obtained The simple sine wave

of Fig 1-11A has been progressively distorted as other sine waves havebeen added to it Whether these are acoustic waves or electronic signals,the process can be reversed The distorted wave of Fig 1-11E can be dis-

assembled, as it were, to the simple f1, f2, and f3sine components by eitheracoustical or electronic filters For example, passing the wave of Fig

1-11E through a filter permitting only f1and rejecting f2and f3, the

origi-nal f1sine wave of Fig 1-11A emerges in pristine condition

Applying names, the sine wave with the lowest frequency (f1) of

Fig 1-11A is called the fundamental, the one with twice the frequency (f2) of Fig 1-11B is called the second harmonic, and the one three times the frequency (f3) of Fig 1-11D is the third harmonic The fourth

harmonic, the fifth harmonic, etc., are four and five times the quency of the fundamental, and so on

fre-Phase

In Fig 1-11, all three components, f1, f2, and f3, start from zero together

This is called an in-phase condition In some cases, the time

relation-A study in the combination of sine waves (relation-A) The fundamental of frequency f1 (B) A

second harmonic of frequency f

1 and half the amplitude of f

1 (E) The waveshape resulting from the addition

of f1 , f2 , and f3 All three components are “in phase,” that is, they all start from zero

at the same instant.

ships between harmonics or between harmonics and the fundamentalare quite different from this Remember how one revolution of thecrankshaft of the automobile engine (360°) was equated with one cycle

of simple harmonic motion of the piston? The up-and-down travel ofthe piston spread out in time traces a sine wave such as that in Fig 1-12.One complete sine-wave cycle represents 360° of rotation If anothersine wave of identical frequency is delayed 90°, its time relationship tothe first one is a quarter wave late (time increasing to the right) A half-wave delay would be 180°, etc For the 360° delay, the wave at the bot-

fre-tom of Fig 1-12 falls in step with the top one, reaching positive peaks and

negative peaks simultaneously and producing the in-phase condition

In Fig 1-11, all three components of the complex wave of Fig 1-11E

are in phase That is, the f1 fundamental, the f2second harmonic, and

the f3third harmonic all start at zero at the same time What happens if

the harmonics are out of phase with the fundamental? Figure 1-13

illus-trates this case The second harmonic f2is now advanced 90°, and the

third harmonic f3 is retarded 90° By combining f1, f2, and f3 for each

instant of time, with due regard to positive and negative signs, the

con-torted wave of Fig 1-13E is obtained

The only difference between Figs 1-11E and 1-13E is that a phase

shift has been introduced between harmonics f2and f3, and the

funda-mental f1 That is all that is needed to produce drastic changes in the

resulting waveshape Curiously, even though the shape of the wave is

dramatically changed by shifting the time relationships of the

compo-nents, the ear is relatively insensitive to such changes In other words,

waves E of Figs 1-11 and 1-13 would sound very much alike to us

A common error is confusing polarity with phase Phase is the time

relationship between two signals while polarity is the / or the /

relationship of a given pair of signal leads

Partials

A musician is inclined to use the term partial instead of harmonic, but

it is best that a distinction be made between the two terms because the

partials of many musical instruments are not harmonically related to

the fundamental That is, partials might not be exact multiples of the

fundamental frequency, yet richness of tone can still be imparted by

such deviations from the true harmonic relationship For example, the

partials of bells, chimes, and piano tones are often in a nonharmonic

relationship to the fundamental

Octaves

Audio and electronics engineers and acousticians frequently use the

integral multiple concept of harmonics, closely allied as it is to the

physical aspect of sound The musician often refers to the octave, a

logarithmic concept that is firmly embedded in musical scales and

ter-minology because of its relationship to the ear’s characteristics Audio

people are also involved with the human ear, hence their common use

of logarithmic scales for frequency, logarithmic measuring units, and