The Physics of Waves

Preface 1 Transverse Waves on a String 1.1 The wave equation for an ideal stretched string 1.2 A general solution of the one-dimensional wave equation 1.3 Harmonic or sinusoidal waves 1.4 Standing sinusoidal waves 1.5 Solving the wave equation by the method of separation of variables 1.6 The general motion of a finite string segment 1.7 Fourier series 1.8 Energy carried by waves on a string 1.9 The reflection and transmission of waves at a discontinuity *1.10 Another derivation of the wave equation for strings *1.11 Momentum carried by a wave 2 Waves on a Membrane 2.1 The wave equation for a stretched membrane 2.2 Standing waves on a rectangular membrane 2.3 Standing waves on a circular membrane 2.4 Interference phenomena with plane traveling waves 3 Introduction to the Theory of Elasticity 3.1 The elongation of a rod 3.2 Volume changes in an elastic medium 3.3 Shear distortion in a plane 3.4 The torsion of round tubes and rods 3.5 The statics of a simple beam 3.6 The bending of a simple beam 3.7 Helical springs 4 One-dimensional Elastic Waves 4.1 Longitudinal waves on a slender rod (a) The wave equation (b) Standing waves (c) Energy and power (d) Momentum transport 4.2 The impedance concept 4.3 Rods with varying cross-sectional area 4.4 The effect of small perturbations on normal-mode frequencies 4.5 Torsional waves on a round rod 4.6 Transverse waves on a slender rod (a) The wave equation (b) Solution of the wave equation (c) Traveling waves (d) Normal-mode vibrations 4.7 Phase and group velocity 4.8 Waves on a helical spring *4.9 Perturbation calculations 5 Acoustic Waves in Fluids 5.1 The wave equation for fluids *5.2 The velocity of sound in gases 5.3 Plane acoustic waves (a) Traveling sinusoidal waves (b) Standing waves of sound 5.4 The cavity (Helmholtz) resonator 5.5 Spherical acoustic waves 5.6 Reflection and refraction at a plane interface 5.7 Standing waves in a rectangular box 5.8 The Doppler effect *5.9 The velocity potential *5.10 Shock Waves *6 Waves on a Liquid Surface 6.1 Basic hydrodynamics (a) Kinematical equations (b) The equation of continuity (c) The Bernoulli equation 6.2 Gravity waves 6.3 Effect of surface tension 6.4 Tidal waves and the tides (a) Tidal waves (b) Tide-generating forces (c) Equilibrium theory of tides (d) The dynamical theory of tides 6.5 Energy and power relations *7 Elastic Waves in Solids 7.1 Tensors and dyadics 7.2 Strain as a dyadic 7.3 Stress as a dyadic 7.4 Hooke's law 7.5 Waves in an isotropic medium (a) Irrotational waves (b) Solenoidal waves 7.6 Energy relations *7.7 Momentum transport by a shear wave *8 Electromagnetic Waves 8.1 Two-conductor transmission line (a) Circuit equations (b) Wave equation (c) Characteristic impedance (d) Reflection from terminal impedance (e) Impedance measurement 8.2 Maxwell's equations 8.3 Plane waves 8.4 Electromagnetic energy and momentum 8.5 Waves in a conducting medium 8.6 Reflection and refraction at a plane interface (a) Boundary conditions (b) Normal incidence on a conductor (c) Oblique incidence on a nonconductor 8.7 Waveguides (a) The vector wave equation (b) General solution for waveguides (c) Rectangular cross section *(d) Circular cross section 8.8 Propagation in ionized gases 8.9 Spherical waves 9 Wave Propagation in Inhomogeneous and Obstructed Media 9.1 The WKB approximation 9.2 Geometrical optics 9.3 The Huygens-Fresnel principle 9.4 Kirchhoff diffraction theory (a) Green's theorem (b) The Helmholtz-Kirchhoff theorem (c) Kirchoff boundary conditions 9.5 Diffraction of transverse waves *9.6 Young's formulation of diffraction 10 Fraunhofer Diffraction 10.1 The paraxial approximation 10.2 The Fraunhofer limit 10.3 The rectangular aperture 10.4 The single slit 10.5 The circular aperture 10.6 The double slit 10.7 Multiple slits *10.8 Practical diffraction gratings for spectral analysis (a) Gratings of arbitrary periodic structure (b) The grating equation (c) Dispersion (d) Resolving power *10.9 Two-dimensional gratings *10.10 Three-dimensional gratings 11 Fresnel Diffraction 11.1 Fresnel zones (a) Circular zones (b) Off-axis diffraction (c) Linear zones 11.2 The rectangular aperture (a) Geometry and notation (b) The Cornu spiral 11.3 The linear slit 11.4 The straight edge 12 Spectrum Analysis of Waveforms 12.1 Nonsinusoidal periodic waves 12.2 Nonrecurrent waves 12.3 Amplitude-modulated waves 12.4 Phase-modulated waves 12.5 The motion of a wave packet in a dispersive medium 12.6 The Fourier transform method 12.7 Properties of transfer functions 12.8 Partial coherence in a wavefield Appendixes A. Vector calculus B. The Smith calculator C. Proof of the uncertainty relation Index