Physics of Vibrations and Waves

ISBN-10: 047001296X

ISBN-13: 9780470012963

Edition: 6th 2005 (Revised)

Authors: H. J. Pain

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Focused on the transmission of energy by wave propagation, in particular electromagnetism, acoustics and optics, this text includes information on matrix applications to coupled oscillations, optical systems and multi-layer dielectric films.
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Book details

List price: $83.00
Edition: 6th
Copyright year: 2005
Publisher: John Wiley & Sons, Incorporated
Publication date: 5/20/2005
Binding: Paperback
Pages: 576
Size: 7.48" wide x 9.69" long x 1.27" tall
Weight: 2.662
Language: English

Introduction to First Edition
Introduction to Second Edition
Introduction to Third Edition
Introduction to Fourth Edition
Introduction to Fifth Edition
Introduction to Sixth Edition
Simple Harmonic Motion
Displacement in Simple Harmonic Motion
Velocity and Acceleration in Simple Harmonic Motion
Energy of a Simple Harmonic Oscillator
Simple Harmonic Oscillations in an Electrical System
Superposition of Two Simple Harmonic Vibrations in One Dimension
Superposition of Two Perpendicular Simple Harmonic Vibrations
Superposition of a Large Number n of Simple Harmonic Vibrations of Equal Amplitude a and Equal Successive Phase Difference [delta]
*Superposition of n Equal SHM Vectors of Length a with Random Phase
Some Useful Mathematics
Damped Simple Harmonic Motion
Methods of Describing the Damping of an Oscillator
The Forced Oscillator
The Operation of i upon a Vector
Vector form of Ohm's Law
The Impedance of a Mechanical Circuit
Behaviour of a Forced Oscillator
Behaviour of Velocity [upsilon] in Magnitude and Phase versus Driving Force Frequency [omega]
Behaviour of Displacement versus Driving Force Frequency [omega]
Problem on Vibration Insulation
Significance of the Two Components of the Displacement Curve
Power Supplied to Oscillator by the Driving Force
Variation of P[subscript av] with [omega]. Absorption Resonance Curve
The Q-Value in Terms of the Resonance Absorption Bandwidth
The Q-Value as an Amplification Factor
The Effect of the Transient Term
Coupled Oscillations
Stiffness (or Capacitance) Coupled Oscillators
Normal Coordinates, Degrees of Freedom and Normal Modes of Vibration
The General Method for Finding Normal Mode Frequencies, Matrices, Eigenvectors and Eigenvalues
Mass or Inductance Coupling
Coupled Oscillations of a Loaded String
The Wave Equation
Transverse Wave Motion
Partial Differentiation
Velocities in Wave Motion
The Wave Equation
Solution of the Wave Equation
Characteristic Impedance of a String (the string as a forced oscillator)
Reflection and Transmission of WAves on a String at a Boundary
Reflection and Transmission of Energy
The Reflected and Transmitted Intensity Coefficients
The Matching of Impedances
Standing Waves on a String of Fixed Length
Energy of a Vibrating String
Energy in Each Normal Mode of a Vibrating String
Standing Wave Ratio
Wave Groups and Group Velocity
Wave Group of Many Components. The Bandwidth Theorem
Transverse Waves in a Periodic Structure
Linear Array of Two Kinds of Atoms in an Ionic Crystal
Absorption of Infrared Radiation by Ionic Crystals
Doppler Effect
Longitudinal Waves
Sound Waves in Gases
Energy Distribution in Sound Waves
Intensity of Sound Waves
Longitudinal Waves in a Solid
Application to Earthquakes
Longitudinal Waves in a Periodic Structure
Reflection and Transmission of Sound Waves at Boundaries
Reflection and Transmission of Sound Intensity
Waves on Transmission Lines
Ideal or Lossless Transmission Line
Coaxial Cables
Characteristic Impedance of a Transmission Line
Reflections from the End of a Transmission Line
Short Circuited Transmission Line (Z[subscript L] = 0)
The Transmission Line as a Filter
Effect of Resistance in a Transmission Line
Characteristic Impedance of a Transmission Line with Resistance
The Diffusion Equation and Energy Absorption in Waves
Wave Equation with Diffusion Effects
Electromagnetic Waves
Maxwell's Equations
Electromagnetic Waves in a Medium having Finite Permeability [mu] and Permittivity [epsilon] but with Conductivity [sigma] = 0
The Wave Equation for Electromagnetic Waves
Illustration of Poynting Vector
Impedance of a Dielectric to Electromagnetic Waves
Electromagnetic Waves in a Medium of Properties [mu], [epsilon] and [sigma] (where [sigma] [not equal] 0)
Skin Depth
Electromagnetic Wave Velocity in a Conductor and Anomalous Dispersion
When is a Medium a Conductor or a Dielectric?
Why will an Electromagnetic Wave not Propagate into a Conductor?
Impedance of a Conducting Medium to Electromagnetic Waves
Reflection and Transmission of Electromagnetic Waves at a Boundary
Reflection from a Conductor (Normal Incidence)
Electromagnetic Waves in a Plasma
Electromagnetic Waves in the Ionosphere
Waves in More than One Dimension
Plane Wave Representation in Two and Three Dimensions
Wave Equation in Two Dimensions
Wave Guides
Normal Modes and the Method of Separation of Variables
Two-Dimensional Case
Three-Dimensional Case
Normal Modes in Two Dimensions on a Rectangular Membrane
Normal Modes in Three Dimensions
Frequency Distribution of Energy Radiated from a Hot Body. Planck's Law
Debye Theory of Specific Heats
Reflection and Transmission of a Three-Dimensional Wave at a Plane Boundary
Total Internal Reflection and Evanescent Waves
Fourier Methods
Fourier Series
Application of Fourier Sine Series to a Triangular Function
Application to the Energy in the Normal Modes of a Vibrating String
Fourier Series Analysis of a Rectangular Velocity Pulse on a String
The Spectrum of a Fourier Series
Fourier Integral
Fourier Transforms
Examples of Fourier Transforms
The Slit Function
The Fourier Transform Applied to Optical Diffraction from a Single Slit
The Gaussian Curve
The Dirac Delta Function, its Sifting Property and its Fourier Transform
The Convolution Theorem
Waves in Optical Systems
Light. Waves or Rays?
Fermat's Principle
The Laws of Reflection
The Law of Refraction
Rays and Wavefronts
Ray Optics and Optical Systems
Power of a Spherical Surface
Magnification by the Spherical Surface
Power of Two Optically Refracting Surfaces
Power of a Thin Lens in Air (Figure 11.12)
Principal Planes and Newton's Equation
Optical Helmholtz Equation for a Conjugate Plane at Infinity
The Deviation Method for (a) Two Lenses and (b) a Thick Lens
The Matrix Method
Interference and Diffraction
Division of Amplitude
Newton's Rings
Michelson's Spectral Interferometer
The Structure of Spectral Lines
Fabry - Perot Interferometer
Resolving Power of the Fabry - Perot Interferometer
Division of Wavefront
Interference from Two Equal Sources of Separation f
Interference from Linear Array of N Equal Sources
Scale of the Intensity Distribution
Intensity Distribution for Interference with Diffraction from N Identical Slits
Fraunhofer Diffraction for Two Equal Slits (N = 2)
Transmission Diffraction Grating (N Large)
Resolving Power of Diffraction Grating
Resolving Power in Terms of the Bandwidth Theorem
Fraunhofer Diffraction from a Rectangular Aperture
Fraunhofer Diffraction from a Circular Aperture
Fraunhofer Far Field Diffraction
The Michelson Stellar Interferometer
The Convolution Array Theorem
The Optical Transfer Function
Fresnel Diffraction
Wave Mechanics
Origins of Modern Quantum Theory
Heisenberg's Uncertainty Principle
Schrodinger's Wave Equation
One-dimensional Infinite Potential Well
Significance of the Amplitude [psi subscript n](x) of the Wave Function
Particle in a Three-dimensional Box
Number of Energy States in Interval E to E + dE
The Potential Step
The Square Potential Well
The Harmonic Oscillator
Electron Waves in a Solid
Non-linear Oscillations and Chaos
Free Vibrations of an Anharmonic Oscillator - Large Amplitude Motion of a Simple Pendulum
Forced Oscillations - Non-linear Restoring Force
Thermal Expansion of a Crystal
Non-linear Effects in Electrical Devices
Electrical Relaxation Oscillators
Chaos in Population Biology
Chaos in a Non-linear Electrical Oscillator
Phase Space
Repellor and Limit Cycle
The Torus in Three-dimensional (x,x,t) Phase Space
Chaotic Response of a Forced Non-linear Mechanical Oscillator
A Brief Review
Chaos in Fluids
Recommended Further Reading
Non-linear Waves, Shocks and Solitons
Non-linear Effects in Acoustic Waves
Shock Front Thickness
Equations of Conservation
Mach Number
Ratios of Gas Properties Across a Shock Front
Strong Shocks
Normal Modes, Phase Space and Statistical Physics
Mathematical Derivation of the Statistical Distributions
Kirchhoff's Integral Theorem
Non-Linear Schrodinger Equation
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