THE MASTER HANDBOOK OF ACOUSTICS This page intentionally left blank. THE MASTER HANDBOOK OF ACOUSTICS
F. Alton Everest
FOURTH EDITION
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DOI: 10.1036/0071399747 To Bonnie Gail, whose love of art, nature, and the author now embraces acoustics. This page intentionally left blank. CONTENTS
Epigraph xxi Introduction xxiii
Chapter 1 Fundamentals of Sound 1
The Simple Sinusoid 2 Sine-Wave Language 3 Propagation of sound 5 The dance of the particles 5 How a sound wave is propagated 7 Sound in free space 9 Wavelength and Frequency 10 Complex Waves 12 Harmonics 12 Phase 12 Partials 15 Octaves 15 The concept of spectrum 17 Electrical, Mechanical, and Acoustical Analogs 20
Chapter 2 Sound Levels and the Decibel 23
Ratios vs. Differences 23 Handling numbers 25 Logarithms 26 Decibels 26 Reference Levels 28 Logarithmic and Exponential Forms Compared 30 Acoustic Power 31
Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use. viii CONTENTS
Using Decibels 33 Example: Sound-pressure level 34 Example: Loudspeaker SPL 34 Example: Microphone specifications 35 Example: Line amplifier 35 Example: General-purpose amplifier 35 Example: Concert hall 35 Example: Combining decibels 36 Ratios and Octaves 37 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 The ear canal 44 The middle ear 45 The inner ear 48 Stereocilia 49 Loudness vs. Frequency 50 Loudness Control 51 Area of Audibility 53 Loudness vs. Sound-Pressure Level 54 Loudness and Bandwidth 56 Loudness of Impulses 59 Audibility of Loudness Changes 61 Pitch vs. Frequency 61 An experiment 63 Timbre vs. Spectrum 63 Localization of Sound Sources 64 Binaural Localization 67 Aural harmonics: Experiment #1 68 Aural harmonics: Experiment #2 69 The missing fundamental 69 The Ear as an Analyzer 70 The Ear as a Measuring Instrument 70 An auditory analyzer: An experiment 71 CONTENTS ix
Meters vs. the Ear 72 The Precedence Effect 73 Perception of Reflected Sound 75 Occupational and Recreational Deafness 76 Summary 79 Chapter 4 Sound Waves in the Free Field 83
Free Sound Field: Definition 83 Sound Divergence 84 Examples: Free-field sound divergence 84 Inverse square in enclosed spaces 87 Hemispherical propagation 88 Chapter 5 Speech, Music, and Noise 89
The Voice System 89 Artificial larynx 89 Sound spectrograph 90 Sound sources for speech 92 Vocal tract molding of speech 92 Formation of voiced sounds 94 Formation of unvoiced sounds 95 Putting it all together 95 Synthesized speech 96 Digital speech synthesis 97 Directionality of speech 98 Music 99 Wind instruments 101 Nonharmonic overtones 101 Dynamic range of speech and music 101 Power in Speech and Music 103 Frequency Range of Speech and Music 104 Future Dynamic-Range Requirements 104 Auditory Area 104 Noise 107 Noise—The good kind 108 Random noise 109 White and pink noise 111 Signal Distortion 112 Harmonic Distortion 114 x CONTENTS
Chapter 6 Analog and Digital Signal Processing 119
Resonance 120 Filters 122 Active filters 123 Analog vs. digital filters 124 Digitization 125 Quantization 126 Digital filters 126 Application of Digital Signal Processing (DSP) 105 Application of DSP to Room Equalization 106
Chapter 7 Reverberation 129
Reverberation and Normal Modes 130 Growth of Sound in a Room 132 Decay of Sound in a Room 134 Idealized Growth and Decay of Sound 134 Reverberation Time 135 Measuring Reverberation Time 137 Impulse Sound Sources 137 Steady-State Sources 138 Equipment 138 Measurement Procedure 140 Analysis of decay traces 140 Mode Decay Variations 142 Writing speed 143 Frequency effect 144 Reverberation Time Variation with Position 145 Acoustically Coupled Spaces 146 Electroacoustically Coupled Spaces 146 Decay rate 147 Eliminating decay fluctuations 147 Influence of Reverberation on Speech 148 Influence of Reverberation on Music 149 Optimum Reverberation Time 150 Bass rise of reverberation time 152 Living room reverberation time 154 CONTENTS xi
Artificial Reverberation: The Past 155 Artificial Reverberation: The Future 156 Arrival Time Gap 157 The Sabine Equation 159 Reverberation calculation: Example 1 160 Reverberation calculation: Example 2 162 Reverberant Field 162
Chapter 8 Control of Interfering Noise 165 Noise Sources and Some Solutions 166 Airborne noise 167 Noise carried by structure 167 Noise transmitted by diaphragm action 168 Sound-insulating walls 168 Porous materials 169 Sound Transmission Classification (STC) 170 Comparison of Wall Structures 171 Double Windows 173 Sound-Insulating Doors 175 Noise and room resonances 176 Active noise control 177
Chapter 9 Absorption of Sound 179 Dissipation of Sound Energy 179 Evaluation of Sound Absorption 181 Reverberation Chamber Method 182 Impedance Tube Method 182 Tone-Burst Method 185 Mounting of Absorbents 186 Mid/High Frequency Absorption by Porosity 187 Glass fiber: Building insulation 189 Glass fiber: Boards 190 Acoustical tile 190 Effect of Thickness of Absorbent 190 Effect of Airspace behind Absorbent 191 Effect of Density of Absorbent 192 xii CONTENTS
Open-Cell Foams 192 Drapes as Sound Absorbers 193 Carpet as Sound Absorber 196 Effect of carpet type on absorbance 199 Effect of carpet underlay on absorbance 200 Carpet absorption coefficients 200 Sound Absorption by People 200 Absorption of Sound in Air 203 Low-Frequency Absorption by Resonance 203 Diaphragmatic Absorbers 205 Polycylindrical Absorbers 209 Poly Construction 212 Membrane Absorbers 213 Helmholtz Resonators 215 Perforated Panel Absorbers 218 Slat Absorbers 224 Placement of Materials 225 Reverberation Time of Helmholtz Resonators 225 Taming room modes 226 Increasing Reverberation Time 229 Modules 229
Chapter 10 Reflection of Sound 235
Reflections from Flat Surfaces 235 Doubling of Pressure at Reflection 237 Reflections from Convex Surfaces 237 Reflections from Concave Surfaces 237 Reflections from Parabolic Surfaces 238 Reflections inside a Cylinder 240 Standing Waves 240 Reflection of Sound from Impedance Irregularities 240 The Corner Reflector 243 Echo-Sounding 243 Perceptive Effects of Reflections 244 CONTENTS xiii
Chapter 11 Diffraction of Sound 245
Rectilinear Propagation 245 Diffraction and Wavelength 246 Diffraction of Sound by Large and Small Apertures 247 Diffraction of Sound by Obstacles 248 Diffraction of Sound by a Slit 249 Diffraction by the Zone Plate 250 Diffraction around the Human Head 251 Diffraction by Loudspeaker Cabinet Edges 253 Diffraction by Various Objects 254
Chapter 12 Refraction of Sound 257
Refraction of Sound 258 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
Chapter 13 Diffusion of Sound 267
The Perfectly Diffuse Sound Field 267 Evaluating Diffusion in a Room 268 Steady-state measurements 268 Decay Beats 269 Exponential Decay 270 Spatial Uniformity of Reverberation Time 271 Decay Shapes 275 Microphone Directivity 275 Room Shape 275 Splaying Room Surfaces 281 Nonrectangular rooms 281 Geometrical Irregularities 282 Absorbent in Patches 282 Concave Surfaces 286 Convex Surfaces: The Poly 286 Plane Surfaces 287 xiv CONTENTS
Chapter 14 The Schroeder Diffusor 289
Schroeder’s First Acoustic Diffusor 290 Maximum-Length Sequences 292 Reflection Phase-Grating Diffusors 292 Quadratic-Residue Diffusors 293 Primitive-Root Diffusors 296 Quadratic-Residue Applications 298 Performance of Diffraction-Grating Diffusors 298 Expansion of the QRD line 304 Solving flutter problems 304 Application of fractals 306 Diffusion in three dimensions 308 Acoustic concrete blocks 309 Measuring diffusion efficiency 311 Comparison of Gratings with Conventional Approaches 312
Chapter 15 Modal Resonances in Enclosed Spaces 317
Resonance in a Pipe 318 Bathroom Acoustics 319 Reflections Indoors 320 Two-Wall Resonance 322 Waves vs. Rays 322 Frequency Regions 323 Dividing the Audio Spectrum 325 Wave Acoustics 326 Mode calculations—An example 328 Experimental Verification 331 Mode Identification 331 Mode Decay 333 Mode Bandwidth 334 Mode Pressure Plots 339 Modal Density 341 Mode Spacing and Coloration 342 Experiments with Colorations 344 Simplified Axial Mode Analysis 346 CONTENTS xv
The Bonello Criterion 348 Controlling Problem Modes 348 Mode Summary 350
Chapter 16 Reflections in Enclosed Spaces 353
Law of the First Wavefront 353 Mean Free Path 354 The effect of single reflections 355 Perception of sound reflections 355 Perception of spaciousness 357 Image changes 357 Discrete echoes 357 Effect of angle of incidence on audibility of reflection 357 Effect of signal type of audibility of reflection 358 Effect of spectrum on audibility of reflection 358 Using reflection data 359 Large Spaces 359 Echoes 359 Spaciousness 360
Chapter 17 Comb-Filter Effects 363
What Is a Comb Filter? 363 Superposition of Sound 364 Tonal Signals and Comb Filters 365 Combing of music and speech signals 367 Combing of direct and reflected sound 368 Comb Filters and Critical Bands 371 Comb Filters in Stereo Listening 374 Coloration and Spaciousness 374 Combing in Stereo Microphone Pickups 375 Audibility of Comb-Filter Effects 375 Comb filters in practice 376 Estimating comb-filter response 380
Chapter 18 Quiet Air for the Studio 385
Selection of Noise Criterion 386 Fan Noise 388 xvi CONTENTS
ASHRAE 389 Machinery Noise 390 Air Velocity 390 Effect of Terminal Fittings 391 “Natural” Attenuation 391 Duct Lining 392 Plenum Silencers 393 Packaged Attenuators 394 Reactive Silencers 394 Resonator Silencer 395 Duct Location 395 Some Practical Suggestions 395
Chapter 19 Acoustics of the Listening Room 399
The Acoustical Link 399 Peculiarities of Small-Room Acoustics 400 Room size 401 Room proportions 401 Reverberation time 403 The Listening Room: Low Frequencies 403 Control of modal resonances 406 Bass traps for the listening room 406 Modal colorations 408 The Listening Room: The Mid-High Frequencies 409 Identification and treatment of reflection points 411 Lateral reflections: Control of spaciousness 413
Chapter 20 Acoustics of the Small Recording Studio 415
Acoustical Characteristics of a Studio 416 Reverberation 418 Studio Design 419 Studio Volume 419 Room Proportions 421 Reverberation Time 422 CONTENTS xvii
Diffusion 423 Noise 424 Studio Design Procedure 424 Some Studio Features 424 Elements Common to all Studios 427
Chapter 21 Acoustics of the Control Room 429
The Initial Time-Delay Gap 429 The Live End 431 Specular Reflections vs. Diffusion 432 Low-Frequency Resonances in the Control Room 434 Initial Time-Delay Gaps in Practice 436 Managing Reflections 438 The Reflection-Free-Zone Control Room 439 Control-Room Frequency Range 441 Outer Shell of the Control Room 442 Inner Shell of the Control Room 442 Representative Control Rooms 442 Some European Designs 444 Consultants 450
Chapter 22 Acoustics for Multitrack Recording 453
Flexibility 545 Advantages of Multitrack 455 Disadvantages of Multitrack 456 Achieving Track Separation 457 Studio Acoustics 458 Distance between artists 458 Microphone management 458 Barriers for separation 459 Electronic separation 459 Electronic instruments and separation 459 The Future of Multichannel 460 Automation 460 xviii CONTENTS
Chapter 23 Audio/Video Tech Room and Voice-Over Recording 461 Selection of Space: External Factors 462 Selection of Space: Internal Factors 462 Work Space Treatment 462 Audio/Video Work Place Example 463 Appraisal of Room Resonances 463 Control of room resonances 464 Treatment of work place 465 Calculations 465 The Voice-Over Booth 468 Dead-End Live-End Voice Studio 468 Voice-Over Booths 468 The Quick Sound Field™ 469
Chapter 24 Adjustable Acoustics 473 Draperies 473 Adjustable Panels: Absorption 474 Adjustable Panels: The Abffusor™ 476 Hinged Panels 478 Louvered Panels 479 Variable Resonant Devices 480 Rotating Elements 483 Portable Units: The Tube Trap™ 484 Portable Units: The Korner Killer™ 485
Chapter 25 Acoustical Distortion 489 Acoustic Distortion and the Perception of Sound 489 Sources of Acoustic Distortion 490 Coupling of room modes 490 Speaker-boundary interference response 491 Comb filtering 493 Poor diffusion 498 Conclusion 500
Chapter 26 Room Acoustics Measurement Software 501 The Evolution of Measurement Technologies 502 CONTENTS xix
Building a Better Analyzer 504 Time-delay spectrometry (TDS) measurement techniques 504 Maximum-length sequence (MLS) techniques 508 AcoustiSoft’s ETF Program 509 Frequency-response measurements 513 Resonance measurements 517 Fractional-octave measurements 520 Energy-time curve measurements 521 Reverberation time 524 Conclusion 526
Chapter 27 Room Optimizer 529
Introduction 529 Modal Response 530 Speaker-Boundary Interference Response 531 Optimization 533 Theory 536 Prediction of room response 536 Optimizing procedure 541 Cost parameter 543 Optimization Procedure 545 Results 549 Stereo pair 549 Stereo pair with two woofers per loudspeaker 550 THX home theater 551 Multichannel music 554 Subwoofer 556 Conclusion 558
Chapter 28 Desktop Auralization 565
Introduction 565 The Auralization Process 569 Summary 581
Appendix 585 Glossary 589 Index 599 This page intentionally left blank. EPIGRAPH
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 explorations 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, First Edition 1877. (Also in first American edition, 1945, courtesy of Dover Publications Inc.)
Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use. This page intentionally left blank. INTRODUCTION
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 fundamentals 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. This page intentionally left blank. CHAPTER 1 Fundamentals of Sound
ound can be defined as a wave motion in air or other elastic Smedia (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. 1
Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use. 2 CHAPTER ONE
The same situation exists between intensity and loudness. The rela- tionship between the two is not linear. This is considered later in more detail 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 in terms of a fundamental and a train of harmonics (or partials) of various amplitudes 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. The 5 weight (mass) on the spring shown in Fig. 1-1 is a vibrating system. If the weight is pulled down to the 5 mark and released, 0 W the spring pulls the weight back toward 0. The weight will not, however, stop at zero; its 5 inertia will carry it beyond 0 almost to 5. The weight will continue to vibrate, or oscil- FIGURE 1-1 late, at an amplitude that will slowly A weight on a spring vibrates at its natural frequency decrease due to frictional losses in the spring, because of the elasticity of the spring and the iner- the air, etc. tia of the weight. The weight in Fig. 1-1 moves in what is called 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-down motion of the pistons beautifully illustrate the relationship between rotary motion and linear simple harmonic motion. The piston position plotted against time produces a sine wave. It is a very basic type of mechanical motion, and it yields an equally basic waveshape in sound and electronics. If a ballpoint pen is fastened to the pointer of Fig. 1-2, and a strip of paper is moved past it at a uniform speed, the resulting trace is a sine wave. 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. FUNDAMENTALS OF SOUND 3
Paper motion
W
Time FIGURE 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.
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 4 CHAPTER ONE
Amplitude relationships for sinusoids