9780470012963

The Physics of Vibrations and Waves, 6th Edition

by
  • ISBN13:

    9780470012963

  • ISBN10:

    047001296X

  • Edition: 6th
  • Format: Paperback
  • Copyright: 2005-06-01
  • Publisher: WILEY
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Summary

The main theme of this highly successful book is that the transmission of energy by wave propogation is fundamental to almost every branch of physics. Therefore, besides giving students a thorough grounding in the theory of waves and vibrations, the book also demonstrates the pattern and unity of a large part of physics. This new edition has been thoroughly revised and has been redeisgned to meet the best contemporary standards. It includes new material on electron waves in solids using the Kronig-Penney model to show how their allowed energies are limited to Brillouin zones, The role of phonons is also discussed. An Optical Transform is used to demonstrate the modern method of lens testing. In the last two chapters the sections on chaos and solitons have been reduced but their essential contents remain. As with earlier editions, the book has a large number of problems together with hints on how to solve them. The Physics of Vibrations and Waves, 6th Edition will prove invaluable for students taking a first full course in the subject across a variety of disciplines particularly physics, engineering and mathematics.

Author Biography

H. J. Pain is a graduate of the united states Naval Aviation Academy, Florida, and of the Universities of St Andrews, London and Aix Marseilles. He taught physics at Imperial College, London where his research interests were in shock waves and magnetohydrodynamics.

Table of Contents

Introduction to First Edition xi
Introduction to Second Edition xii
Introduction to Third Edition xiii
Introduction to Fourth Edition xiv
Introduction to Fifth Edition xv
Introduction to Sixth Edition xvi
Simple Harmonic Motion
1(36)
Displacement in Simple Harmonic Motion
4(2)
Velocity and Acceleration in Simple Harmonic Motion
6(2)
Energy of a Simple Harmonic Oscillator
8(2)
Simple Harmonic Oscillations in an Electrical System
10(2)
Superposition of Two Simple Harmonic Vibrations in One Dimension
12(3)
Superposition of Two Perpendicular Simple Harmonic Vibrations
15(2)
*Polarization
17(3)
Superposition of a Large Number n of Simple Harmonic Vibrations of Equal Amplitude a and Equal Successive Phase Difference δ
20(2)
*Superposition of n Equal SHM Vectors of Length a with Random Phase
22(3)
Some Useful Mathematics
25(12)
Damped Simple Harmonic Motion
37(16)
Methods of Describing the Damping of an Oscillator
43(10)
The Forced Oscillator
53(26)
The Operation of i upon a Vector
53(1)
Vector form of Ohm's Law
54(2)
The Impedance of a Mechanical Circuit
56(1)
Behaviour of a Forced Oscillator
57(3)
Behaviour of Velocity v in Magnitude and Phase versus Driving Force Frequency ω
60(2)
Behaviour of Displacement versus Driving Force Frequency ω
62(2)
Problem on Vibration Insulation
64(2)
Significance of the Two Components of the Displacement Curve
66(2)
Power Supplied to Oscillator by the Driving Force
68(1)
Variation of Pav with ω. Absorption Resonance Curve
69(1)
The Q-Value in Terms of the Resonance Absorption Bandwidth
70(1)
The Q-Value as an Amplification Factor
71(3)
The Effect of the Transient Term
74(5)
Coupled Oscillations
79(28)
Stiffness (or Capacitance) Coupled Oscillators
79(2)
Normal Coordinates, Degrees of Freedom and Normal Modes of Vibration
81(5)
The General Method for Finding Normal Mode Frequencies, Matrices, Eigenvectors and Eigenvalues
86(1)
Mass or Inductance Coupling
87(3)
Coupled Oscillations of a Loaded String
90(5)
The Wave Equation
95(12)
Transverse Wave Motion
107(44)
Partial Differentiation
107(1)
Waves
108(1)
Velocities in Wave Motion
109(1)
The Wave Equation
110(2)
Solution of the Wave Equation
112(3)
Characteristic Impedance of a String (the string as a forced oscillator)
115(2)
Reflection and Transmission of Waves on a String at a Boundary
117(3)
Reflection and Transmission of Energy
120(1)
The Reflected and Transmitted Intensity Coefficients
120(1)
The Matching of Impedances
121(3)
Standing Waves on a String of Fixed Length
124(2)
Energy of a Vibrating String
126(1)
Energy in Each Normal Mode of a Vibrating String
127(1)
Standing Wave Ratio
128(1)
Wave Groups and Group Velocity
128(4)
Wave Group of Many Components. The Bandwidth Theorem
132(3)
Transverse Waves in a Periodic Structure
135(3)
Linear Array of Two Kinds of Atoms in an Ionic Crystal
138(2)
Absorption of Infrared Radiation by Ionic Crystals
140(1)
Doppler Effect
141(10)
Longitudinal Waves
151(20)
Sound Waves in Gases
151(4)
Energy Distribution in Sound Waves
155(2)
Intensity of Sound Waves
157(2)
Longitudinal Waves in a Solid
159(2)
Application to Earthquakes
161(1)
Longitudinal Waves in a Periodic Structure
162(1)
Reflection and Transmission of Sound Waves at Boundaries
163(1)
Reflection and Transmission of Sound Intensity
164(7)
Waves on Transmission Lines
171(28)
Ideal or Lossless Transmission Line
173(1)
Coaxial Cables
174(1)
Characteristic Impedance of a Transmission Line
175(2)
Reflections from the End of a Transmission Line
177(1)
Short Circuited Transmission Line (ZL = 0)
178(1)
The Transmission Line as a Filter
179(4)
Effect of Resistance in a Transmission Line
183(3)
Characteristic Impedance of a Transmission Line with Resistance
186(1)
The Diffusion Equation and Energy Absorption in Waves
187(3)
Wave Equation with Diffusion Effects
190(1)
Appendix
191(8)
Electromagnetic Waves
199(40)
Maxwell's Equations
199(3)
Electromagnetic Waves in a Medium having Finite Permeability μ and Permittivity ε but with Conductivity σ = 0
202(2)
The Wave Equation for Electromagnetic Waves
204(2)
Illustration of Poynting Vector
206(1)
Impedance of a Dielectric to Electromagnetic Waves
207(1)
Electromagnetic Waves in a Medium of Properties μ, ε and σ (where σ ≠ 0)
208(3)
Skin Depth
211(1)
Electromagnetic Wave Velocity in a Conductor and Anomalous Dispersion
211(1)
When is a Medium a Conductor or a Dielectric?
212(2)
Why will an Electromagnetic Wave not Propagate into a Conductor?
214(1)
Impedance of a Conducting Medium to Electromagnetic Waves
215(2)
Reflection and Transmission of Electromagnetic Waves at a Boundary
217(5)
Reflection from a Conductor (Normal Incidence)
222(1)
Electromagnetic Waves in a Plasma
223(4)
Electromagnetic Waves in the Ionosphere
227(12)
Waves in More than One Dimension
239(28)
Plane Wave Representation in Two and Three Dimensions
239(1)
Wave Equation in Two Dimensions
240(2)
Wave Guides
242(3)
Normal Modes and the Method of Separation of Variables
245(1)
Two-Dimensional Case
246(1)
Three-Dimensional Case
247(1)
Normal Modes in Two Dimensions on a Rectangular Membrane
247(3)
Normal Modes in Three Dimensions
250(1)
Frequency Distribution of Energy Radiated from a Hot Body. Planck's Law
251(2)
Debye Theory of Specific Heats
253(1)
Reflection and Transmission of a Three-Dimensional Wave at a Plane Boundary
254(2)
Total Internal Reflection and Evanescent Waves
256(11)
Fourier Methods
267(38)
Fourier Series
267(7)
Application of Fourier Sine Series to a Triangular Function
274(1)
Application to the Energy in the Normal Modes of a Vibrating String
275(3)
Fourier Series Analysis of a Rectangular Velocity Pulse on a String
278(3)
The Spectrum of a Fourier Series
281(2)
Fourier Integral
283(2)
Fourier Transforms
285(1)
Examples of Fourier Transforms
286(1)
The Slit Function
286(1)
The Fourier Transform Applied to Optical Diffraction from a Single Slit
287(2)
The Gaussian Curve
289(3)
The Dirac Delta Function, its Sifting Property and its Fourier Transform
292(1)
Convolution
292(5)
The Convolution Theorem
297(8)
Waves in Optical Systems
305(28)
Light, Waves or Rays?
305(2)
Fermat's Principle
307(1)
The Laws of Reflection
307(2)
The Law of Refraction
309(1)
Rays and Wavefronts
310(3)
Ray Optics and Optical Systems
313(1)
Power of a Spherical Surface
314(2)
Magnification by the Spherical Surface
316(1)
Power of Two Optically Refracting Surfaces
317(1)
Power of a Thin Lens in Air (Figure 11.12)
318(2)
Principal Planes and Newton's Equation
320(1)
Optical Helmholtz Equation for a Conjugate Plane at Infinity
321(1)
The Deviation Method for (a) Two Lenses and (b) a Thick Lens
322(3)
The Matrix Method
325(8)
Interference and Diffraction
333(78)
Interference
333(1)
Division of Amplitude
334(3)
Newton's Rings
337(1)
Michelson's Spectral Interferometer
338(2)
The Structure of Spectral Lines
340(1)
Fabry - Perot Interferometer
341(2)
Resolving Power of the Fabry - Perot Interferometer
343(12)
Division of Wavefront
355(2)
Interference from Two Equal Sources of Separation f
357(6)
Interference from Linear Array of N Equal Sources
363(3)
Diffraction
366(3)
Scale of the Intensity Distribution
369(1)
Intensity Distribution for Interference with Diffraction from N Identical Slits
370(2)
Fraunhofer Diffraction for Two Equal Slits (N = 2)
372(1)
Transmission Diffraction Grating (N Large)
373(1)
Resolving Power of Diffraction Grating
374(2)
Resolving Power in Terms of the Bandwidth Theorem
376(1)
Fraunhofer Diffraction from a Rectangular Aperture
377(2)
Fraunhofer Diffraction from a Circular Aperture
379(4)
Fraunhofer Far Field Diffraction
383(3)
The Michelson Stellar Interferometer
386(2)
The Convolution Array Theorem
388(3)
The Optical Transfer Function
391(4)
Fresnel Diffraction
395(8)
Holography
403(8)
Wave Mechanics
411(48)
Origins of Modern Quantum Theory
411(3)
Heisenberg's Uncertainty Principle
414(3)
Schrodinger's Wave Equation
417(2)
One-dimensional Infinite Potential Well
419(3)
Significance of the Amplitude Ψ n(x) of the Wave Function
422(2)
Particle in a Three-dimensional Box
424(1)
Number of Energy States in Interval E to E + dE
425(1)
The Potential Step
426(8)
The Square Potential Well
434(4)
The Harmonic Oscillator
438(3)
Electron Waves in a Solid
441(9)
Phonons
450(9)
Non-linear Oscillations and Chaos
459(46)
Free Vibrations of an Anharmonic Oscillator - Large Amplitude Motion of a Simple Pendulum
459(1)
Forced Oscillations - Non-linear Restoring Force
460(3)
Thermal Expansion of a Crystal
463(2)
Non-linear Effects in Electrical Devices
465(2)
Electrical Relaxation Oscillators
467(2)
Chaos in Population Biology
469(8)
Chaos in a Non-linear Electrical Oscillator
477(4)
Phase Space
481(4)
Repellor and Limit Cycle
485(1)
The Torus in Three-dimensional (x,x,t) Phase Space
485(2)
Chaotic Response of a Forced Non-linear Mechanical Oscillator
487(1)
A Brief Review
488(6)
Chaos in Fluids
494(10)
Recommended Further Reading
504(1)
References
504(1)
Non-linear Waves, Shocks and Solitons
505(28)
Non-linear Effects in Acoustic Waves
505(3)
Shock Front Thickness
508(1)
Equations of Conservation
509(1)
Mach Number
510(1)
Ratios of Gas Properties Across a Shock Front
511(1)
Strong Shocks
512(1)
Solitons
513(18)
Bibliography
531(1)
References
531(2)
Appendix 1: Normal Modes, Phase Space and Statistical Physics
533(14)
Mathematical Derivation of the Statistical Distributions
542(5)
Appendix 2: Kirchhoff's Integral Theorem
547(4)
Appendix 3: Non-Linear Schrodinger Equation
551(1)
Index 552

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