Introduction to Vibrations and Waves 1st Edition by H John Pain, Patricia Rankin ISBN 1118441109 9781118441107
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ISBN 10: 1118441109
ISBN 13: 9781118441107
Author: H John Pain, Patricia Rankin
Based on the successful multi-edition book “The Physics of Vibrations and Waves” by John Pain, the authors carry over the simplicity and logic of the approach taken in the original first edition with its focus on the patterns underlying and connecting so many aspects of physical behavior, whilst bringing the subject up-to-date so it is relevant to teaching in the 21st century.
The transmission of energy by wave propagation is a key concept that has applications in almost every branch of physics with transmitting mediums essentially acting as a continuum of coupled oscillators. The characterization of these simple oscillators in terms of three parameters related to the storage, exchange, and dissipation of energy forms the basis of this book. The text moves naturally on from a discussion of basic concepts such as damped oscillations, diffraction and interference to more advanced topics such as transmission lines and attenuation, wave guides, diffusion, Fourier series, and electromagnetic waves in dielectrics and conductors. Throughout the text the emphasis on the underlying principles helps readers to develop their physics insight as an aid to problem solving.
This book provides undergraduate students of physics and engineering with the mathematical tools required for full mastery of the concepts. With worked examples presented throughout the text, as well as the Problem sets concluding each chapter, this textbook will enable students to develop their skills and measure their understanding of each topic step-by-step.
A companion website is also available, which includes solutions to chapter problems and PowerPoint slides.
Review of “The Physics of Vibrations and Waves 6e“
This is an excellent textbook, full of interesting material clearly explained and fully worthy of being studied by future contributors …” Journal of Sound and Vibration
Introduction to Vibrations and Waves 1st Table of contents:
1 Simple Harmonic Motion
1.1 Displacement in Simple Harmonic Motion
1.2 Velocity and Acceleration in Simple Harmonic Motion
1.3 Energy of a Simple Harmonic Oscillator
1.4 Simple Harmonic Oscillations in an Electrical System
1.5 Superposition of Two Simple Harmonic Vibrations in One Dimension
2 Damped Simple Harmonic Motion
Introduction
2.1 Complex Numbers
2.2 The Exponential Series
2.3 Methods of Describing the Damping of an Oscillator
3 The Forced Oscillator
Introduction
3.1 The Operation of i upon a Vector
3.2 Vector Form of Ohm’s Law
3.3 The Tuned LCR Circuit
3.4 Power Supplied to Oscillator by the Input Voltage
3.5 The Q-Value in Terms of the Resonance Absorption Bandwidth
3.6 The Forced Mechanical Oscillator
3.7 Behaviour of Velocity v in Magnitude and Phase versus Driving Force Frequency ω
3.8 Behaviour of Displacement x versus Driving Force Frequency ω
3.9 The Q-Value as an Amplification Factor
3.10 Significance of the Two Components of the Displacement Curve
3.11 Problem on Vibration Insulation
3.12 The Effect of the Transient Term
4 Coupled Oscillations
Introduction
4.1 Stiffness (or Capacitance) Coupled Oscillators
4.2 Normal Modes of Vibration, Normal Coordinates and Degrees of Freedom
4.3 Mass or Inductance Coupling
4.4 Coupled Oscillations of a Loaded String
4.5 The Wave Equation
5 Transverse Wave Motion (1)
Introduction
5.1 Partial Differentiation
5.2 Waves
5.3 Velocities in Wave Motion
5.4 The Wave Equation
5.5 Solution of the Wave Equation
5.6 Characteristic Impedance of a String (the String as a Forced Oscillator)
5.7 Reflection and Transmission of Waves on a String at a Boundary
5.8 Reflection and Transmission of Energy
5.9 The Reflected and Transmitted Intensity Coefficients
5.10 Matching of Impedances
5.11 Standing Waves on a String of Fixed Length
5.12 Standing Wave Ratio
5.13 Energy in Each Normal Mode of a Vibrating String
6 Transverse Wave Motion (2)
Introduction
6.1 Wave Groups, Group Velocity and Dispersion
6.2 Wave Group of Many Components. The Bandwidth Theorem
6.3 Heisenberg’s Uncertainty Principle
6.4 Transverse Waves in Periodic Structures (1) Waves in a Crystal
6.5 Linear Array of Two Kinds of Atoms in an Ionic Crystal
6.6 Transverse Waves in Periodic Structures (2) The Diffusion Equation, Energy Loss from Wave Systems
7 Longitudinal Waves
Introduction
7.1 Sound Waves in Gases
7.2 Energy Distribution in Sound Waves
7.3 Intensity of Sound Waves
7.4 Longitudinal Waves in a Solid
7.5 Application to Earthquakes
7.6 Reflection and Transmission of Sound Waves at Boundaries
7.7 Reflection and Transmission of Sound Intensity
7.8 Water Waves
7.9 Doppler Effect
8 Waves on Transmission Lines
Introduction
8.1 Ideal or Lossless Transmission Line
8.2 Coaxial Cables
8.3 Characteristic Impedance of a Transmission Line
8.4 Reflections from the End of a Transmission Line
8.5 Short Circuited Transmission Line (ZL = 0)
8.6 The Transmission Line as a Filter
8.7 Effect of Resistance in a Transmission Line
8.8 Characteristic Impedance of a Transmission Line with Resistance
8.9 Matching Impedances
9 Electromagnetic Waves
Introduction
9.1 Maxwell’s Equations
9.2 Electromagnetic Waves in a Medium having Finite Permeability μ and Permittivity ε but with Conductivity σ = 0
9.3 The Wave Equation for Electromagnetic Waves
9.4 Illustration of Poynting Vector
9.5 Impedance of a Dielectric to Electromagnetic Waves
9.6 Electromagnetic Waves in a Medium of Properties μ, ε and σ (where σ ≠ 0)
9.7 Skin Depth
9.8 Electromagnetic Wave Velocity in a Conductor and Anomalous Dispersion
9.9 When is a Medium a Conductor or a Dielectric?
9.10 Why will an Electromagnetic Wave not Propagate into a Conductor?
9.11 Impedance of a Conducting Medium to Electromagnetic Waves
9.12 Reflection and Transmission of Electromagnetic Waves at a Boundary
9.13 Reflection from a Conductor (Normal Incidence)
10 Waves in More Than One Dimension
Introduction
10.1 Plane Wave Representation in Two and Three Dimensions
10.2 Wave Equation in Two Dimensions
10.3 Wave Guides
10.4 Normal Modes and the Method of Separation of Variables
10.5 Two-Dimensional Case
10.6 Three-Dimensional Case
10.7 Normal Modes in Two Dimensions on a Rectangular Membrane
10.8 Normal Modes in Three Dimensions
10.9 3D Normal Frequency Modes and the de Broglie Wavelength
10.10 Frequency Distribution of Energy Radiated from a Hot Body. Planck’s Law
10.11 Debye Theory of Specific Heats
11 Fourier Methods
11.1 Fourier Series
11.2 Application of Fourier Sine Series to a Triangular Function
11.3 Application to the Energy in the Normal Modes of a Vibrating String
11.4 Fourier Series Analysis of a Rectangular Velocity Pulse on a String
11.5 Three-Phase Full Wave Rectification
11.6 The Spectrum of a Fourier Series
12 Waves in Optics (1) Interference
12.1 Light: Waves or Rays?
12.2 Fermat’s Principle
12.3 The Laws of Reflection
12.4 The Law of Refraction
12.5 Interference and Diffraction
12.6 Interference
12.7 Division of Amplitude
12.8 Newton’s Rings
12.9 Michelson’s Spectral Interferometer
12.10 The Structure of Spectral Lines
12.11 Fabry–Pérot Interferometer
12.12 Resolving Power of the Fabry–Pérot Interferometer
12.13 Division of Wavefront
12.14 Interference from Two Equal Sources of Separation f
12.15 Interference from Linear Array of N Equal Sources
13 Waves in Optics (2) Diffraction
13.1 Diffraction
13.2 Scale of the Intensity Distribution
13.3 Intensity Distribution for Interference with Diffraction from N Identical Slits
13.4 Fraunhofer Diffraction for Two Equal Slits (N = 2)
13.5 Transmission Diffraction Grating (N Large)
13.6 Resolving Power of Diffraction Grating
13.7 Resolving Power in Terms of the Bandwidth Theorem
13.8 Fraunhofer Diffraction from a Rectangular Aperture
13.9 Fraunhofer Diffraction from a Circular Aperture
13.10 The Airy Disc and Resolving Power
13.11 The Michelson Stellar Interferometer
13.12 Fresnel Diffraction
13.13 Zone Plate
13.14 Electron Diffraction and Brillouin Zones
14 Non-linear Oscillations
14.1 Free Vibrations of an Anharmonic Oscillator – Large Amplitude Motion of a Simple Pendulum
14.2 Forced Oscillations – Non-linear Restoring Force
14.3 Thermal Expansion of a Crystal
14.4 Non-linear Acoustic Waves and Shocks
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Tags: H John Pain, Patricia Rankin, Vibrations, Waves