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Fundamentals of Waves and Oscillations

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Paperback | 26 September 1988

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Paperback
612 Pages

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23 x 18.5 x 4

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This textbook, addressed primarily to physics and engineering students, is a comprehensive introduction to waves and oscillations, both mechanical and electromagnetic. Elementary aspects of matter waves are also considered. One objective is to illustrate the physics involved in the description and analysis of waves through a wide range of examples, from purely mechanical and purely electromagnetic to coupled electro-mechanical waves, such as plasma oscillations and hydromagnetic waves. In this process, the use of complex amplitudes in the mathematical analysis is illuminated and encouraged to make tractable a wider range of problems than is ordinarily considered in an introductory text. General concepts and wave phenomena such as wave energy and momentum, interference, diffraction, scattering, dispersion, and the Doppler effect are illustrated by numerous examples and demonstrations. Among the special topics covered are waves on periodic structures and in solids, wave guides, a detailed analysis of light scattering from thermal fluctuations of a liquid surface, and feedback instabilities. Important ideas and equations are displayed in boxes for easy reference, and there are numerous examples throughout the text and exercises at the end of every chapter. Undergraduates and graduates should find this an indispensable account of this central subject in science and engineering.

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You Can Find This Book In

Non-Fiction Science Science in General Physics Classical Mathematics Wave Mechanics including Vibration & Acoustics Materials & States of Matter

Preface	p. xi
Oscillations
Review of elementary concepts and examples	p. 3
Introduction	p. 3
Harmonic motion defined	p. 4
The mass--spring oscillator	p. 7
Examples of harmonic motion	p. 11
The two-body oscillator. Reduced mass	p. 19
Two-dimensional oscillator	p. 24
Nonlinear oscillations	p. 26
Forced harmonic motion	p. 28
Free damped motion	p. 31
Problems	p. 32
The complex amplitude	p. 37
A review of complex numbers	p. 37
Euler's formula	p. 40
The complex amplitude of a harmonic function	p. 43
Discussion	p. 47
Examples	p. 48
Problems	p. 50
Forced oscillations and frequency response	p. 51
Electro-mechanical analogies	p. 51
Frequency response	p. 53
Impedance and admittance	p. 64
Power transfer	p. 67
Sources of vibration	p. 70
Examples	p. 71
Fourier analysis	p. 72
Arbitrary driving force	p. 81
Examples	p. 82
Problems	p. 87
Free oscillations and impulse response	p. 92
Free oscillations	p. 92
Impulse response	p. 99
Response to an arbitrary driving force	p. 101
Transition to steady state	p. 103
Discussion	p. 107
Examples	p. 109
Problems	p. 111
Coupled oscillators	p. 113
Forced harmonic motion	p. 113
Free motion. Normal modes	p. 121
Weakly coupled oscillators. Beats	p. 125
Impulse response	p. 129
Orthogonality. Configuration space	p. 134
Unequal coupled oscillators	p. 138
Examples	p. 147
Problems	p. 147
Waves
Fundamentals of waves	p. 153
What is a wave?	p. 153
Description of waves (kinematics)	p. 154
Dynamics. Field equations	p. 166
Harmonic waves and complex amplitude equations	p. 173
Examples of waves	p. 177
Simple demonstrations	p. 180
Wave power	p. 182
Wave pulse	p. 185
Waves in two and three dimensions	p. 187
Examples	p. 190
Problems	p. 192
Wave reflection, transmission, and absorption	p. 197
Wave reflection at a junction	p. 197
Energy absorption at a termination	p. 203
Wave reflection and elastic collisions	p. 208
Examples	p. 209
Problems	p. 210
Resonances and normal modes	p. 213
Forced harmonic waves	p. 213
Forced harmonic motion of the real mass-spring oscillator	p. 217
Free oscillations and normal modes	p. 219
Normal mode expansion. Fourier series	p. 225
Continuous harmonic force distribution	p. 235
Normal modes in two and three dimensions	p. 238
Density of normal modes	p. 240
Examples	p. 241
Problems	p. 242
Electromagnetic waves	p. 246
Review of units	p. 246
EM waves on a cable reconsidered	p. 250
Maxwell's equations	p. 253
Plane EM waves	p. 255
Generation of EM waves	p. 258
Polarization	p. 266
Dispersion of EM waves	p. 274
Examples	p. 282
Problems	p. 283
Acoustic waves in fluids	p. 286
Description of fluid motion	p. 286
Fluid equations	p. 288
Acoustic field equations	p. 291
Spherical waves	p. 295
The acoustic spectrum	p. 298
Measurements	p. 299
Problems	p. 304
Wave interference and diffraction	p. 306
Interference of two plane waves	p. 306
Interference of waves from an array of sources	p. 311
Continuous source distribution	p. 319
Diffraction	p. 324
Diffraction limited resolution	p. 332
Coherence and incoherence	p. 336
Examples	p. 337
Problems	p. 341
Refraction and reflection	p. 343
Trace velocity and Snell's law	p. 343
Acoustic reflection and transmission coefficients	p. 346
EM reflection and transmission coefficients	p. 349
Total reflection	p. 352
Refraction in a moving medium	p. 354
Inhomogeneous medium	p. 356
Examples	p. 361
Problems	p. 363
The Doppler effect	p. 366
Mechanical waves	p. 366
Electromagnetic waves	p. 376
Problems	p. 381
Periodic structures. Dispersion	p. 383
Wave transmission on a mass-spring lattice	p. 383
Wave packet and group velocity	p. 388
Wave impedance and energy flow	p. 395
Wave attenuation	p. 397
Normal modes of a one-dimensional lattice	p. 400
General motion and impulse response of a periodic lattice	p. 404
Problems	p. 406
Wave guides and cavities	p. 409
Propagating and decaying waves	p. 409
Acoustic waves in a rectangular wave guide	p. 414
EM waves in a rectangular wave guide	p. 421
Normal modes in a rectangular cavity	p. 425
Problems	p. 427
Matter waves	p. 430
Review	p. 430
Free particle wave function	p. 433
The Uncertainty Principle	p. 435
Effect of potential. Barrier penetration	p. 437
Refraction of matter waves	p. 440
Stationary states. Schroedinger equation	p. 442
Problems	p. 447
Special Topics
Radiation and scattering	p. 451
Sound radiation from a pulsating sphere	p. 451
Multipole sources	p. 455
Nonuniform spherical source. Spherical harmonics	p. 459
Radiation from a continuous source distribution	p. 464
Huygens' principle and scattering	p. 467
Acoustic scattering	p. 468
Electromagnetic scattering	p. 472
Problems	p. 475
Surface waves on a liquid	p. 478
Waves on shallow water	p. 478
Surface tension	p. 484
Waves on deep water. Effect of surface tension	p. 488
Effect of viscosity	p. 492
Thermal ripples and Brillouin scattering	p. 495
Liquid-liquid interface. Critical phenomenon	p. 503
Problems	p. 505
Plasma oscillations and hydromagnetic waves	p. 507
The plasma state	p. 507
Longitudinal waves. (Plasma oscillations)	p. 511
Transverse waves. (Hydromagnetic or Alfven waves)	p. 517
Problems	p. 521
Waves in solids	p. 523
Longitudinal waves in a rod	p. 523
Shear waves	p. 527
Wave reflection. Energy considerations	p. 529
Bending waves on a plate	p. 530
Displacement, deformation, and rotation	p. 534
Stress-strain relation	p. 540
Relations between elastic constants	p. 543
Longitudinal and transverse waves	p. 545
Wave conversion	p. 549
The Rayleigh wave	p. 551
Seismology	p. 555
Problems	p. 558
Feedback oscillations	p. 560
The frequency equation	p. 560
Valve instability	p. 565
Instability of a vortex sheet	p. 573
Whistles and wind instruments	p. 578
Lasers	p. 585
Heat maintained oscillations. The Rijke tube	p. 586
Examples	p. 588
Problems	p. 589
Index	p. 591
Table of Contents provided by Syndetics. All Rights Reserved.

Fundamentals of Waves and Oscillations

At a Glance

Paperback

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Defective items

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