Book:C.A. Coulson/Waves/Seventh Edition

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C.A. Coulson: Waves: A Mathematical Account of the Common Type of Wave Motion (7th Edition)

Published $\text {1955}$, Oliver and Boyd.


Subject Matter


Contents

Preface (January 1941)
Preface to Seventh Edition (May 1955)
chapter $\text {I}$. THE EQUATION OF WAVE MOTION
Introductory
General Form of Progressive Waves
Harmonic Waves
Plane Waves
The Equation of Wave Motion
Principle of Superposition
Special Types of Solution
List of Solutions
Equation of Telegraphy
Exponential Form of Harmonic Waves
A Solved Example
Examples
chapter $\text {II}$. WAVES ON STRINGS
The Differential Equation
Kinetic and Potential Energies
Inclusion of Initial Conditions
Reflection at a Change of Density
Alternative Solutions
Strings of Finite Length, Normal Modes
String Plucked at its Mid-point
The Energies of the Normal Modes
Normal Co-ordinates
String with Load at its Mid-point
The Energies of the Normal Modes
Normal Co-ordinates
String with Load at its Mid-point
Damped Vibrations
Method of Reduction to a Steady Wave
Examples
chapter $\text {III}$. WAVES IN MEMBRANES
The Differential Equation
Solution for a Rectangular Membrane
Normal Co-ordinates for Rectangular Membranes
Circular Membrane
Examples
chapter $\text {IV}$. LONGITUDINAL WAVES IN BARS AND SPRINGS
Differential Equation for Waves along a Bar
Free Vibrations of a Finite Bar
Vibrations of a Clamped Bar
Normal Co-ordinates
Case of a Bar in a state of Tension
Vibrations of a Loaded Spring
Examples
chapter $\text {V}$. WAVES IN LIQUIDS
Summary of Hydrodynamical Formulæ
Tidal Waves and Surface Waves
Tidal Waves, General Conditions
Tidal Waves in a Straight Channel
Tidal Waves on Lakes and Tanks
Tidal Waves on Rectangular and Circular Tanks
Paths of the Particles
Method of Reduction to a Steady Wave
Surface Waves, the Velocity Potential
Surface Waves on a Long Rectangular Tank
Surface Waves in Two Dimensions
Paths of the Particles
The Kinetic and Potential Energies
Rate of Transmission of Energy
Inclusion of Surface Tension. General Formulæ
Capillary Waves in One Dimension
Examples
chapter $\text {VI}$. SOUND WAVES
Relation between Pressure and Density
Differential Equation in Terms of Condensation
Boundary Conditions
Solutions for a Pipe of Finite Length
Normal Modes in a Tube with Movable Boundary
The Velocity Potential, General Formulæ
The Differential Equation of Wave Motion
Stationary Waves in a Tube of Finite Length
The Kinetic and Potential Energies
Progressive Waves in a Tube of Varying Section
Examples
chapter $\text {VII}$. ELECTRIC WAVES
Maxwell's Equations
Non-conducting Media, the Equation of Wave Motion
Electric and Magnetic Potentials
Plane Polarised Waves in a Dielectric Medium
Rate of Transmission of Energy in Plane Waves
Reflection and Refraction of Light Waves
Internal Reflection
Partially Conducting Media, Plane Waves
Reflection from a Metal
Radiation Pressure
Skin Effect
Examples
chapter $\text {VIII}$. GENERAL CONSIDERATIONS
Doppler Effect
Beats
Amplitude Modulation
Group Velocity
Motion of Wave Packets
Kirchhoff's Solution of the Equation of Wave Motion
Fresnel's Principle
Diffraction at a pin-hole
Fraunhofer Diffraction Theory
Retarded Potential Theory
Examples
Index


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