An Introduction to Acoustics

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ISBN: 9780486442518 | 0486442519
Cover: Paperback
Copyright: 4/26/2005

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This undergraduate-level text opens with an overview of fundamental particle vibration theory, and it proceeds to examinations of waves in air and in three dimensions, interference patterns and diffraction, and acoustic impedance, as illustrated in the behavior of horns. Supplementary sections include four appendixes and answers to problems. 1951 edition.

INTRODUCTION

(8)

I-1 Sound vs acoustics

(1)

I-2 Vibrating bodies

(1)

I-3 Frequency

(1)

I-4 Amplitude

(1)

I-5 Waves

(1)

I-6 Wavelength. Frequency in the wave

(1)

I-7 The principle of superposition

(1)

I-8 Energy density. Intensity in the wave

(1)

I-9 Sound "quality"

(1)

I-10 The use of electrical analogs

(1)

I-11 Waves in solids

(1)

I-12 Experimental technique

(1)

I-13 Applied acoustics

(1)

I-14 Systems of units

(2)

CHAPTER 1. FUNDAMENTAL PARTICLE VIBRATION THEORY

(28)

1-1 Simple harmonic motion of a particle

(1)

1-2 Energy in SHM

(1)

1-3 Combinations of SHM's along the same straight line

(2)

1-4 Two collinear SHM's whose frequencies differ by a small amount Beats

(2)

1-5 Mathematical vs audible beats

(1)

1-6 Combinations of more than two SHM's of different frequencies

(1)

1-7 Fourier's theorem

(1)

1-8 Determination of the Fourier coefficients

(2)

1-9 Even and odd functions

(1)

1-10 Convergence

(1)

1-11 Application of the Fourier analysis to empirical functions

(1)

1-12 Damped vibrations of a particle

(1)

1-13 Case I. Large frictional force

(1)

1-14 Case II. Small frictional force

(1)

1-15 Case III. Critical damping

(1)

1-16 Forced vibrations

(1)

1-17 The differential equation

(1)

1-18 The steady state solution for forced vibrations

(2)

1-19 Velocity and displacement resonance

(1)

1-20 The amplitude at resonance

(1)

1-21 Phase relationships

(1)

1-22 Energy transfer in forced oscillations

(1)

1-23 Some applications of the theory of forced vibrations

(2)

1-24 The importance of the transient response

(1)

1-25 Superposition of SHM's mutually perpendicular

(4)

CHAPTER 2. PLANE WAVES IN AIR

(18)

2-1 Introduction

(1)

2-2 Dilatation and condensation

(1)

2-3 Bulk modulus

(1)

2-4 Significant variables in the field of sound

(1)

2-5 The differential equation for plane waves

(2)

2-6 Physical significance of the particle displacement

(1)

2-7 Solution of the wave equation

(2)

2-8 Disturbances of a periodic nature

(1)

2-9 The wavelength

(1)

2-10 Graphical representation

(1)

2-11 Waves containing more than one frequency component

(1)

2-12 Alternate forms for the steady state solution to the wave equation

(1)

2-13 Phase relationships

(1)

2-14 Energy in the wave

(1)

2-15 Kinetic energy

(1)

2-16 Potential energy

(2)

2-17 Total energy density in the wave

(1)

2-18 Sound intensity

(1)

2-19 Units of intensity

(1)

2-20 The decibel

(1)

2-21 Intensity "level"; pressure "level"

(3)

CHAPTER 3. WAVES IN THREE DIMENSIONS

(19)

3-1 Waves in three dimensions. The equation of continuity

(1)

3-2 Application of Newton's second law

(1)

3-3 The differential equation for waves in three dimensions

(1)

3-4 The differential equation for spherical waves

(1)

3-5 The solution of the differential equation

(1)

3-6 The velocity potential, Φ

(2)

3-7 Application of the function Φ The "pulsing sphere"

(1)

3-8 Intensity for spherical waves

(1)

3-9 The "strength" of a source

(1)

3-10 Sources equivalent to a pulsing sphere

(1)

3-11 Limitations on the use of the "strength of source" concept

(1)

3-12 Extension of the "strength of source" concept

(1)

3-13 The double source

(1)

3-14 Examples of the double source

(1)

3-15 Radiation from a double source as a function of frequency

(1)

3-16 Quantitative analysis of the double source

(2)

3-17 Comparison of total power radiated by different types of sources

(1)

3-18 Practical double sources. The principle of the baffle

(3)

CHAPTER 4. INTERFERENCE PATTERNS. DIFFRACTION

(25)

4-1 Definition of interference for wave motion

(1)

4-2 Diffraction

(1)

4-3 Diffraction in acoustics and in light

(1)

4-4 Importance of the ratio of wavelength to dimension

(1)

4-5 The single slit pattern. Simplifying assumptions

(1)

4-6 Application of Huygens' Principle

(1)

4-7 Vector method of determining the acoustic pressure at point a

(1)

4-8 Essential geometry and equations

(1)

4-9 The variation of pm, with theta

(1)

4-10 The variation of (pm)² with the polar angle

(1)

4-11 Representation of intensity distribution on a polar graph

(2)

4-12 General significance of the diffraction pattern for a single slit

(1)

4-13 Openings of other shapes. The short rectangle or the square

(1)

4-14 Diffraction pattern for a circular aperture

(2)

4-15 Practical examples of the diffraction pattern for a circular aperture

(1)

4-16 Multiple slits and openings

(1)

4-17 Diffraction effects around the edges of obstructions

(1)

4-18 Fresnel laminar zones

(2)

4-19 The Fresnel integrals. The spiral of Cornu

(2)

4-20 Use of the Cornu spiral to determine the diffraction pattern for a straight edge

(1)

4-21 Direct graph of intensity

(1)

4-22 The shape of the diffraction pattern, as a function of λ

(1)

4-23 Diffraction of waves around obstacles of various contours lying in a field of sound

(2)

4-24 Diffraction effects for an acoustic piston set in a circular plate of finite size

(1)

4-25 General conclusions on diffraction

(2)

CHAPTER 5. ACOUSTIC IMPEDANCE. BEHAVIOR OF HORNS

(29)

5-1 The principle of analog

(1)

5-2 Types of analogies

(2)

5-3 Sound radiation and acoustic impedance

101

(1)

5-4 Elements of complex notation as applied to electrical circuits

101

(2)

5-5 Specific acoustic impedance

103

(1)

5-6 Specific acoustic impedance for plane waves

104

(2)

5-7 Analogous acoustic impedance

106

(1)

5-8 Specific acoustic impedance for spherical waves

106

(1)

5-9 The Helmholtz resonator

107

(3)

5-10 The resonance frequency

110

(1)

5-11 The behavior of horns

111

(1)

5-12 Radiation into a cylindrical tube closed at one end

112

(2)

5-13 Force on the piston. Total radiation impedance

114

(1)

5-14 Tube open at one end

114

(2)

5-15 Horns

116

(1)

5-16 The conical horn

117

(1)

5-17 Transmission coefficient for a horn

118

(1)

5-18 The exponential horn

119

(2)

5-19 Transmission coefficient for an exponential horn. Comparison with the conical horn

121

(1)

5-20 Effect of reflections upon horn behavior

122

(1)

5-21 The horn as an impedance matching device

122

(1)

5-22 The "hornless" or direct-radiator loudspeaker. Specific acoustic impedance at the surface

122

(3)

5-23 Distribution pattern for energy leaving horns or direct radiators

125

(1)

5-24 General significance of acoustic impedance for radiation

125

(3)

CHAPTER 6. LONGITUDINAL WAVES IN DIFFERENT GASES. WAVES IN LIQUIDS AND SOLIDS

128

(23)

6-1 Isothermal and adiabatic bulk modulus for an ideal gas

128

(1)

6-2 Factors affecting the velocity of longitudinal waves in gases

129

(2)

6-3 Experimental determination of the velocity of sound waves in gases

131

(1)

6-4 Transmission of longitudinal waves through gases as related to kinetic theory

132

(2)

6-5 Waves of large amplitude

134

(3)

6-6 Miscellaneous open-air effects

137

(1)

6-7 Acoustic focusing devices. Mirrors and lenses

138

(3)

6-8 Attenuation of longitudinal waves in gases

141

(1)

6-9 The Doppler effect

142

(1)

6-10 Practical importance of the Doppler effect

143

(2)

6-11 Transmission of longitudinal waves through liquids

145

(1)

6-12 Experimental measurement of c for liquids

145

(1)

6-13 Attenuation effects in liquids

146

(1)

6-14 Longitudinal waves in solids

147

(2)

6-15 The measurement of c as a means of studying the elastic properties of solids

149

(1)

6-16 Dissipation within solids

149

(2)

CHAPTER 7. STATIONARY WAVES. VIBRATING SOURCES. MUSICAL INSTRUMENTS

151

(33)

7-1 Introduction

151

(1)

7-2 The ideal string

152

(1)

7-3 The differential equation

153

(1)

7-4 The solution

154

(1)

7-5 The string of limited length

154

(1)

7-6 Reflection at one end of a string

155

(1)

7-7 Simultaneous reflection at both ends of a string

156

(1)

7-8 Vibrating string fixed at both ends

157

(1)

7-9 Interpretation of the stationary wave equation

158

(1)

7-10 Other end conditions. Both ends free

159

(3)

7-11 Vibrating string, one end fixed, one end free

162

(1)

7-12 Initial conditions

163

(1)

7-13 Other initial conditions

164

(2)

7-14 Bowing. Relaxation oscillations

166

(1)

7-15 Vibration of membranes. Stationary waves in two dimensions

166

(2)

7-16 Longitudinal stationary waves in bars

168

(1)

7-17 Transverse waves in bars

169

(2)

7-18 The tuning fork

171

(1)

7-19 The vibration of plates

172

(1)

7-20 Stationary air waves in pipes

172

(1)

7-21 Vibrations in a pipe closed at both ends

173

(1)

7-22 Vibration of an open organ pipe

174

(1)

7-23 Reflection and acoustic impedance

175

(1)

7-24 Frequencies of vibration of a "closed" organ pipe

176

(1)

7-25 General features of stringed instruments. The violin

176

(3)

7-26 The piano

179

(1)

7-27 The wind instruments. Excitation of an organ pipe

180

(1)

7-28 Wind instruments of the reed type

181

(1)

7-29 Wind instruments as radiating sources of sound

182

(2)

CHAPTER 8. REFLECTION AND ABSORPTION OF SOUND WAVES

184

(18)

8-1 Introduction

184

(1)

8-2 Reflection of longitudinal waves at a boundary between two ideal elastic media, each infinite, in extent

184

(2)

8-3 Relative magnitudes of the particle velocities

186

(1)

8-4 Relative phases

187

(1)

8-5 Magnitudes and phases of the acoustic pressures

187

(1)

8-6 Practical implications

188

(2)

8-7 The effect of partial reflection upon the stationary wave pattern

190

(2)

8-8 The absorption coefficient

192

(1)

8-9 Specific acoustic impedance of a boundary surface

193

(1)

8-10 Both media perfectly elastic and infinite in extent

193

(1)

8-11 Boundaries for which zn is reactive

193

(2)

8-12 Specific acoustic impedance at positions of discontinuity in the tube cross section

195

(1)

8-13 Specific acoustic impedance at the surface of absorbing materials

196

(1)

8-14 The relation between zn, and the absorption coefficient for plane air waves of normal incidence

196

(1)

8-15 Other absorption coefficients

197

(2)

8-16 Use of panel resonance

199

(1)

8-17 Absorbing "layers." The effect of thickness

199

(1)

8-18 Good reflectors and good absorbers

200

(2)

CHAPTER 9. SPEECH AND HEARING

202

(28)

9-1 Importance of the subjective element in acoustics

202

(1)

9-2 The vocal apparatus

202

(1)

9-3 The speech process

203

(2)

9-4 The vocoder

205

(1)

9-5 Energy distribution in speech as a function of frequency

206

(1)

9-6 Intelligibility of speech as related to frequency band width

207

(1)

9-7 Miscellaneous voice properties

208

(1)

9-8 Artificial voices

208

(1)

9-9 The hearing process

208

(1)

9-10 The structure of the ear

209

(1)

9-11 The organ of Corti

210

(1)

9-12 Mechanical properties of the cochlea: Resonance theory of Helm-holtz

211

(1)

9-13 Other resonance theories

211

(1)

9-14 The organs of sensation

212

(1)

9-15 Frequency perception

213

(1)

9-16 Hearing data for the normal ear

214

(1)

9-17 Threshold of audibility

214

(1)

9-18 Loudness and loudness level

215

(3)

9-19 Differential intensity level sensitivity of the ear

218

(1)

9-20 Pitch vs frequency

218

(1)

9-21 Differential frequency sensitivity of the ear

219

(1)

9-22 Shift in pitch (or apparent frequency) at high intensities

220

(1)

9-23 Masking

221

(1)

9-24 Sum and difference frequencies

222

(1)

9-25 The response of the ear to a harmonic series

223

(1)

9-26 The importance of the transient period to sound quality. Phase effects

224

(1)

9-27 Binaural effects

225

(1)

9-28 Hearing defects

226

(1)

9-29 Musical intervals. Scales

226

(2)

9-30 Consonance and dissonance

228

(2)

CHAPTER 10. SOUND MEASUREMENTS. EXPERIMENTAL ACOUSTICS

230

(30)

10-1 Precise acoustic measurement

230

(1)

10-2 Free-space measurements. Anechoic rooms

230

(3)

10-3 Reverberant chambers

233

(1)

10-4 Standard sound sources. The thermophone

233

(1)

10-5 The pistonphone

234

(1)

10-6 The electrostatic actuator

235

(1)

10-7 Measurements in a field of sound. The Rayleigh disk

236

(2)

10-8 Other absolute detection methods

238

(1)

10-9 Detectors requiring calibration. Microphones

239

(1)

10-10 Microphones

240

(6)

10-11 Relative sensitivities of different types of microphones

246

(1)

10-12 The calibration of microphones

246

(1)

10-13 The reciprocity method for calibrating microphones

247

(2)

10-14 Measurement of frequency in a wave

249

(1)

10-15 Complex wave analysis

250

(2)

10-16 Noise. The continuous acoustic spectrum

252

(2)

10-17 The measurement of acoustic impedance

254

(4)

10-18 Conclusion

258

(2)

CHAPTER 11. REPRODUCTION OF SOUND

260

(31)

11-1 Introduction

260

(1)

11-2 The general problem

261

(1)

11-3 An ideal transducer

262

(2)

11-4 Early types of transducers

264

(2)

11-5 Transducer with electromagnetic drive

266

(1)

11-6 "Blocked" vs "motional" impedance

266

(1)

11-7 Motional impedance and mechanical impedance

267

(1)

11-8 Motional impedance and acoustic radiation

268

(2)

11-9 Behavior of the transducer in a vacuum tube circuit

270

(2)

11-10 Behavior of the cone vs the acoustic piston

272

(1)

11-11 Acoustic coupling problems

273

(1)

11-12 Back of cone completely enclosed

274

(1)

11-13 Loudspeaker cabinet with open back

275

(1)

11-14 The acoustic phase inverter

276

(2)

11-15 The half wavelength pipe

278

(1)

11-16 The use of horns

279

(1)

11-17 High frequency radiation problems. Multiple loudspeakers

280

(2)

11-18 Effect of room resonances

282

(1)

11-19 Electrical equalization circuits

283

(1)

11-20 Transducers for disk phonograph records

284

(1)

11-21 Differences in transfer behavior

285

(1)

11-22 Mechanical impedance of moving parts. Tracking

286

(2)

11-23 Conclusion

288

(3)

CHAPTER 12. MISCELLANEOUS APPLIED ACOUSTICS

291

(28)

12-1 The acoustic properties of rooms

291

(1)

12-2 An ideal reverberant room

292

(1)

12-3 Rate of disappearance of energy from the ideal reverberant room

292

(1)

12-4 The steady state energy density

293

(1)

12-5 The transient equations

294

(2)

12-6 Reverberation time

296

(1)

12-7 Partially live rooms

297

(1)

12-8 Determination of αs

297

(1)

12-9 Effect of varying frequency

298

(1)

12-10 Absorbing surfaces of limited area

298

(1)

12-11 Computation of αs from zn

299

(1)

12-12 Effect of room resonances. Steady state

299

(1)

12-13 Normal modes of vibration. The transient period

300

(1)

12-14 Transmission of wave energy through partitions

301

(1)

12-15 Acoustic filters

302

(5)

12-16 Ultrasonics

307

(1)

12-17 Ultrasonic sources

308

(1)

12-18 Piezoelectric generators

309

(2)

12-19 Detectors of ultrasonic waves

311

(1)

12-20 Coupling between transducer and medium

312

(1)

12-21 Undersea signaling and ranging

313

(1)

12-22 Diffraction of light by liquids carrying ultrasonic waves

314

(1)

12-23 Testing of materials with ultrasonic waves

315

(1)

12-24 Other industrial applications of ultrasonic waves

316

(1)

12-25 Biological effects of ultrasonic waves

317

(1)

12-26 Acoustics in relation to other branches of physics

317

(2)

APPENDIX I. THE INTRODUCTION OF T11E VELOCITY POTENTIAL, Φ, INTO THE DIFFERENTIAL EQUATION FOR SPACE WAVES

319

(2)

APPENDIX II. THE RELATIONSHIP BETWEEN THE VELOCITY POTENTIAL Φ AND THE CONDENSATION, s

321

(2)

APPENDIX III. TABLE OF FRESNEL INTEGRALS

323

(1)

APPENDIX IV. DERIVATION OF THE EXPRESSION, U = eic/4 (Eq. 12-1)

324

(2)

LIST OF SYMBOLS

326

(3)

REFERENCES

329

(2)

INDEX

331

(6)

ANSWERS TO PROBLEMS

337

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An Introduction to Acoustics

Summary

Table of Contents

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