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

Subject Matter

 * Wave Mechanics

Contents

 * Preface (January 1941)
 * Preface to Seventh Edition (May 1955)


 * $\text {I}$. 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


 * $\text {II}$. 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


 * $\text {III}$. WAVES IN MEMBRANES
 * The Differential Equation
 * Solution for a Rectangular Membrane
 * Normal Co-ordinates for Rectangular Membranes
 * Circular Membrane
 * Examples


 * $\text {IV}$. 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


 * $\text {V}$. 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


 * $\text {VI}$. 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


 * $\text {VII}$. 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


 * $\text {VIII}$. 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



Source work progress
* : Chapter $\text {I}$: The Equation of Wave Motion: $\S 6$