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

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## C.A. Coulson:

## 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

## Further Editions

- 1941: C.A. Coulson:
*Waves* - 1943: C.A. Coulson:
*Waves*(2nd ed.) - 1944: C.A. Coulson:
*Waves*(3rd ed.) - 1947: C.A. Coulson:
*Waves*(4th ed.) - 1949: C.A. Coulson:
*Waves*(5th ed.) - 1952: C.A. Coulson:
*Waves*(6th ed.)

## Source work progress

- 1955: C.A. Coulson:
*Waves*(7th ed.) ... (next): Chapter $\text {I}$: The Equation of Wave Motion: $\S 2$