Thomas D. Rossing Northern Illinois University I h n

SECOND EDITION

The Science of Sound

• • T

Addison-Wesley Publishing Company

Reading, Massachusetts • Menlo Park, California New York • Don Mills, Ontario • Wokingham, England

Amsterdam • Bonn • Sydney • Singapore • Tokyo • Madrid • San Juan

Contents

PARTI Motion, Energy, Waves, and Other Physical Principles

Chapter 1 Motion, Force, and Energy

2.3 2.4 2.5

2.6 2.7 2.8

Simple vibrating systems Systems with two or three masses Systems with many modes of vibration Vibrations in musical instruments Complex vibrations: vibration spectra Summary

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 .10

]hap

2.1 2.2

Distance Speed and velocity Graphical representation of Acceleration Force, mass, and Newton's Pressure Work and energy Power Units Summary

ter 2 Vibrating Systems

Simple harmonic motion Energy and damping

motion

laws

3 4 6 8

10 11 12 14 15 16

19 21

Chapter 3 Waves

3.1 3.2 3.3 3.4 3.5 3.6

3.7 3.8 3.9

3.10 3.11 3.12

What is a wave? Progressive waves Impulsive waves: reflection Superposition and interference Sound waves Wave propagation in two and three dimensions The Doppler effect Reflection Refraction Diffraction Interference Summary

22 23

26 27 30 30

33 34 36 38 40

41 43 45 46 47 48 49

ix

x Contents

Chapter 4 Resonance

4.1 Resonance of a mass-spring vibrator 53 4.2 Phase of driven vibrations 54 4.3 Standing waves on a string 54 4.4 Partials, harmonics, and overtones 56 4.5 Open and closed pipes 57 4.6 Acoustic impedance 59 4.7 Helmholtz resonator 60 4.8 Sympathetic vibrations: soundboards 60 4.9 Summary 61

PART II 6 3

Perception and Measurement of Sound

Chapter 5 Hearing

5.1 The hearing function 5.2 Structure of the ear 5.3 Signal processing in the auditory

system 5.4 Critical bands 5.5 Binaural hearing and localization 5.6 Measuring sensations: psychophysics 5.7 Logarithms and powers of ten 5.8 Subjective attributes of sound 5.9 Summary

65 66

72 74 75 76 77 80 80

7.7 7.8 7.9

7.10 7.11

7.12 7.13 7.14 7.15

Chai \_.IIrt|

8.1 8.2 8.3

Chapter 6 Sound Pressure, Power, and Loudness

6.1 6.2 6.3 6.4 6.5 6.6

6.7 6.8

Sound pressure level Sound power and intensity levels Multiple sources Loudness level Loudness of pure tones: sones Loudness of complex tones: critical bands Loudness of combined sounds Musical dynamics and loudness

85 87 89 92 93

95 97 99

6.9 Masking 101 6.10 Loudness reduction by masking 104 6.11 Loudness and duration: impulsive

sounds and adaptation 105 6.12 Summary 106

Chapter 7 Pitch and Timbre

7.1 Pitch scales 109 7.2 Pitch discrimination 111 7.3 Pitch of pure tones 111 7.4 Pitch of complex tones: virtual pitch 114 7.5 Seebeck's siren and Ohm's law:

a historical note 115 Theories of pitch: place pitch vs. periodicity pitch 117 Absolute pitch 122 Pitch standards 124 Timbre or tone quality 125 Fourier analysis of complex tones 127 Timbre and dynamic effects: envelope and duration 130 Tristimulus diagrams 133 Vibrato 134 Blend of complex tones 135 Summary 137

Chapter 8 Combination Tones and Harmony

Linear superposition 143 Phase angle 144 Combination of two simple harmonic motions 145

8.4 Pure tones with slightly different frequencies: beats 147

8.5 The musical staff: musicians' graph paper 149

8.6 Combination tones 151 8.7 Modulation of one tone by another 152 8.8 Other nonlinear effects: aural

harmonics and summation tones 153 8.9 Origin of difference tones 154

5.10 Consonance and dissonance: musical intervals 155

Contents xi

8.11 The effect of phase on timbre 161 8.12 Beats of mistuned consonances 162 8.13 The central nervous system:

autocorrelation and crosscorrelation 163 8.14 Cerebral dominance 164 8.15 Summary 165

PART III 169 Acoustics of Musical Instruments

Chapter 9 Musical Scales and Temperament

9.1 The scale of just intonation 9.2 The Pythagorean scale 9.3 Meantone temperament 9.4 Equal temperament 9.5 Tuning to equal temperament 9.6 Electronic tuners 9.7 Intonation 9.8 Summary

Chapter 10 String Instruments

10.1 Construction of the violin 10.2 Vibrations of a plucked string 10.3 Vibrations of a bowed string 10.4 Vibrations of the violin body 10.5 Tuning the top and back plates 10.6 The bridge 10.7 Other bowed string instruments 10.8 Music and physics: a new family

of fiddles 10.9 Construction of the guitar

10.10 The guitar as a vibrating system 10.11 Vibrations of the top plate, back

plate, and air cavity 10.12 Resonances of the guitar body 10.13 Sound radiation 10.14 The electric guitar

172 174 176 177 178 180 182 183

188 189 190 195 197 199 200

200 201 203

204 205 207 209

Instruments of the brass family Oscillations in a pipe Pressure-controlled valves The bell and mouthpiece Valves and slides: filling in between the modes The French horn The trombone Tuba, baritone, and fluegelhorn The spectra of brass instruments Mutes Wall material Summary

218 219 221 223

226 228 229 230 230 231 233 234

10.15 Strings, frets, and compensation 10.16 Summary

Chapter 11 Brass Instruments

11.1 11.2 11.3 11.4 11.5

11.6 11.7 11.8 11.9

11.10 11.11 11.12

Chapter 12 Woodwind Instruments

12.1 How a pipe-reed system vibrates 12.2 Tone holes 12.3 Bore types 12.4 The clarinet 12.5 Registers and register holes 12.6 The double reeds 12.7 The saxophone 12.8 Oscillating air streams and whistles 12.9 The flute

12.10 The recorder 12.11 Organ pipes 12.12 Summary

Chapter 13 Percussion Instruments

13.1 Vibrations of bars 13.2 Rectangular bars: the glockenspiel 13.3 The marimba, xylophone, and vibes 13.4 Chimes 13.5 Triangles 13.6 Vibrations of membranes 13.7 Timpani 13.8 Bass drum and snare drum

211 212

238 241 243 244 246 247 249 250 251 253 254 254

258 260 262 264 266 267 268 271

xii Contents

13.9 13.10 13.11 13.12 13.13 13.14 13.15 13.16

Other drums Vibrations of plates Cymbals Gongs and tamtams Steel drums Bells and carillons Handbells Summary

273 274 275 277 278 280 282 283

Chapter 14 Keyboard Instruments

14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9

14.10 14.11 14.12 14.13

Construction of the piano Inharmonicity in piano strings The tuning of unisons Piano sound Hammer-string interaction The clavichord The harpsichord The harp The pipe organ: its construction Organ pipes Sound generation in flue pipes Tuning and voicing organ pipes Summary

287 290 293 293 294 295 296 298 298 299 302 303 305

PART IV 509 The Human Voice

Chapter 15 Speech Production

15.1 15.2 15.3 15.4 15.5

15.6 15.7 15.8 15.9

15.10

The vocal organs The larynx and the vocal chords The vocal tract Articulation of speech Resonances of the vocal tract: formants Models of the vocal tract Studies of the vocal tract Prosodic features of speech Demonstration experiments Summary

311 312 315 317

319 320 323 324 324 326

Chapter 16 Speech Recognition, Analysis, and Synthesis

16.1 16.2 16.3 16.4

16.5 16.6 16.7 16.8

16.9

The analysis of speech The recognition of vowels The recognition of consonants Filtered speech and noisy environments The synthesis of speech Time-domain vs. frequency-domain Speech recognition by computers Speaker identification by speech spectrograms: voiceprints Summary

329 331 332

336 338 340 341

342 343

Chapter 17 Singing

17.1 17.2

17.3 17.4 17.5 17.6

17.7 17.8

Formants and pitch Differences between spoken and sung vowels Formant tuning by sopranos Breathing and air flow Registers, voices, and muscles Other factors influencing the spectra of sung notes Choir singing Summary

348

349 353 355 357

360 362 364

PART V 3 6 7 The Electrical Production of Sound

Chapter 18 A Little about Electricity

18.1 Electrical circuits 369 18.2 Electrical energy and power 373 18.3 Alternating current 374 18.4 Electrical resonance 376 18.5 Diodes 378 18.6 Transformers 379

Contents xüi

18.7 18.8

Power supplies Summary

Chapter 19 Filters, Amplifiers,

19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8

and Oscillators

Filters Amplifiers Distortion in amplifiers Feedback Operational amplifiers Oscillators Function generators Summary

379 380

21.10 Multiple tracks 21.11 Digital tape recording 21.12 Summary

429 430 431

Chapter 20 Microphones and Loudspeakers

20.1 Microphones as transducers 20.2 Velocity microphones 20.3 Unidirectional microphones 20.4 Microphone impedance 20.5 Microphone sensitivity 20.6 Loudspeakers as transducers 20.7 Structure of dynamic loudspeakers 20.8 Air suspension 20.9 Baffles and enclosures

20.10 Horn loudspeakers 20.11 Multispeaker systems 20.12 Other loudspeaker types 20.13 Loudspeaker efficiency 20.14 Summary

Chapter 21 The Recording and Reproduction of Sound

21.1 Disc recording 21.2 Recording characteristics 21.3 Dynamic range 21.4 Phonograph pickups 21.5 Stereophonic discs 21.6 Magnetic tape recording 21.7 Tape speed and frequency response 21.8 Bias and equalization 21.9 Tape noise

Chapter 22 Components for High-Fidelity Sound 383 385 386 388 388 389 390 390

394 397 397 398 399 401 402 404 404 409 410 412 413 414

n

419 420 420 421 422 423 425 427 428

22.1

22.2 22.3 22.4 22.5 22.6 22.7 22.8 22.9

22.10

22.11 22.12

The components of a high-fidelity sound system Record players Tone arms and cartridges Tape decks AM/FM tuners Stereo broadcasting Amplifiers Distortion Amplifier power and distortion Loudspeaker efficiency and distortion Earphones (headphones) Summary

PART VI The Acoustics of Rooms

Chapt

23.1

23.2 23.3

23.4 23.5

23.6 23.7 23.8 23.9

23.10 23.11

er 23 Auditorium Acoustics

Sound propagation outdoors and indoors

436 437 438 440 441 443 444 447 449

450 451 452

457

459 Direct, early, and reverberant sound 460 Direct and early sound: the precedence effect Reverberant sound Calculation of the reverberation time Air absorption Criteria for good acoustics Background noise Avery Fisher Hall: a case study Variable acoustics Summary

462 463

466 468 469 473 473 475 475

xiv Contents

Chapter 24 Electronic Reinforcement of Sound

24.1 Sound sources in a room 480 24.2 Sound fields 480 24.3 Power considerations 483 24.4 Loudspeaker placement 484 24.5 Loudspeaker directivity 485 24.6 Acoustic feedback 487 24.7 Equalization 488 24.8 Time delay 490 24.9 Enhancement of reverberation 490

24.10 Outdoor sound systems 492 24.11 Summary 492

26.3 26.4 26.5 26.6 26.7 26.8 26.9

26.10

26.11 26.12

Electromechanical tone generators Electronic tone generators Frequency dividers Voicing and keying Other features of electronic organs Electronic pianos Electronic carillons Amplification of conventional instruments Tone-modification circuits Summary

523 524 525 527 528 530 531

531 532 534

Chapter 25 High-Fidelity Sound-Reproducing Systems

25.1 Acoustics of small rooms 495 25.2 Sound images from multiple sources 498 25.3 What is high-fidelity sound? 503 25.4 Single- and multi-channel

sound-reproducing systems 504 25.5 Stereophonic sound 505 25.6 The sound field in listening rooms 508 25.7 Testing and equalizing the listening

room 510 25.8 Quadraphonic sound 511 25.9 Time delay and ambience

synthesizers 512 25.10 Listening with earphones 514 25.11 Let the ear judge! 514 25.12 Summary 515

PART VII 519 Electronic Music

Chapter 26 Electronic Organs and Other Musical Instruments

26.1 Early instruments 26.2 Electronic organs

522 522

Chapter 27 Electronic Music Synthesizers

27.1 The development of synthesizers 537 27.2 Voltage-controlled oscillators

and amplifiers 539 27.3 Voltage-controlled filters 542 27.4 Control characteristics and sources 544 27.5 The keyboard and other control

voltage sources 544 27.6 Ring modulators 546 27.7 Other modules 548 27.8 The organization of a synthesizer 548 27.9 Computer-controlled synthesizers 550

27.10 FM music synthesis 551 27.11 Summary 552

Chapter 28 Digital Techniques for Generating and Recording Sound

28.1 Music by numbers: digital representation of sound 556

28.2 Sampling and digital conversion 556 28.3 Aliasing 557 28.4 Quantization error and dither 558 28.5 Digital tone generators 558 28.6 Digital filtering 562 28.7 Digital recording 563 28.8 Digital recording on magnetic tape 566 28.9 Digital audio tape recorders for

home use 567 28.10 Compact disc digital audio 568

Contents xv

Chapter 29 Digital Computers and Musical Sound

29.1

29.2

29.3 29.4 29.5 29.6

29.7 29.8 29.9

29.10 29.11 29.12 29.13

Digital computers: electronic brains or high-speed morons? The organization of a digital computer Memory Programming a digital computer Computer synthesis of music Smaller and smaller: the development of microelectronics Digital synthesizers Hybrid digital/analog synthesizers Drum synthesizers MIDI Digital electronic organs Digital generation of organ tone Summary

577

578 579 581 582

585 586 589 591 591 592 592 595

31.7 Other psychological effects 624 31.8 The physiological effects of noise 625 31.9 Summary 625

Chapt

32.1

32.2 32.3 32.4 32.5 32.6 32.7 32.8 32.9

32.10 32.11 32.12 32.13

гг 32 The Control of Noise

Analyzing a noise problem: source-path-receiver Noise regulations Exposure to occupational noise Product labeling Walls and floors Barriers—indoors and outdoors Enclosures Sound absorbers Heating and air-conditioning noise Aircraft noise Supersonic aircraft Ultrasound and infrasound Summary

629 630 632 633 633 635 638 639 640 642 644 645 646

PART VIII 599 Environmental Noise

Chapter 30 Noise in the Environment

30.1 Sound power and mechanical power 602 30.2 Noise levels 603 30.3 Sound propagation outdoors 604 30.4 Flow noise 606 30.5 Machinery noise 607 30.6 Indoor noise 608 30.7 Motor vehicles 609 30.8 Railroads and aircraft 611 30.9 Summary 612

Chapter 31 The Effects of Noise on People

31.1 Temporary hearing loss 31.2 Permanent hearing loss 31.3 Ear damage 31.4 Hearing protectors 31.5 Speech interference 31.6 Interference with sleep

615 618 619 620 621 623

Chapter 33 Measuring Instruments

33.1 The cathode-ray oscilloscope 649 33.2 The audio generator 651 33.3 The function generator 651 33.4 Electronic tuners 652 33.5 The frequency counter 652 33.6 The sound level meter 653 33.7 The spectrum analyzer 653 33.8 Distortion analyzers 654 33.9 The level recorder 655

33.10 The impedance tube 656

Appendix

A.l Units: SI and other systems 657 A.2 Powers of ten and logarithms 659 A.3 Solving equations 660 A.4 Graphs 661 A. 5 Decibels 662 A.6 A proposal for three new clefs 668 A.7 Notation used for notes 669

Answers to Odd-Numbered Problems 671 Index 677