Preface
Part I. Introduction: 1. Sound pulses
2. The equations of motion
3. The wave equation
4. The effect of body forces
5. Boundary conditions
6. Poisson's solution of the initial-value problem
Part II. Wave Fronts and Characteristics: 1. Introduction
2. Space-time
3. Characteristics and geometrical optics
4. The uniqueness theorem: dependence and influence domains
5. Diffraction
6. Reflected fronts
Appendix: the characteristics containing a given 2-space
caustics
Part III. Geometrical Acoustics: 1. Introduction
2. Weak solutions of the wave equation
3. The propagation of discontinuities
4. The propagation of algebraic infinities
5. Geometrical acoustics
6. Geometrical acoustics in a homogenous medium
7. The transport equations of higher order
8. The superposition principle
9. Series expansions related to geometrical acoustics
Appendix: the focusing of acoustic shocks
Part IV. The Application of Geometrical Acoustics to Reflexion Problems: 1. Introduction
2. Reflexion of a plane pulse
3. Reflexion of a spherical pulse by a surface of revolution
4. Series expansion of a reflected pulse
5. Reflexion of a spherical pulse by a paraboloid
7. Series expansion of the reflected pulse
8. The refraction of a spherical pulse at a plane interface
Appendix: the reflexion of a spherical acoustic shock wave
Part V. The Diffraction of a Pulse by a Wedge: 1. Introduction
2. The Green's function of the wedge
3. Construction of the Green's function
4. An alternative form of the Green's function
5. Diffraction of a plane pulse
6. The half-plane
7. Some diffraction problems related to the half-plane problem
Appendix: elementary solutions and Green's function
Part VI. Some Other Diffraction Problems: 1. Introduction
2. The Green's function of the circular cylinder
3. The eigenfunction expansion
4. The diffraction formulae
5. Diffraction of a plane pulse
6. The Green's function of the sphere
7. Approximate evaluation of the diffracted field
8. Geometrical optics in a stratified medium
9. Pulse diffraction in a stratified medium
Appendix: Asymptotic behaviour of the eigenvalues and eigenfunctions of the circular cylinder
Bibliography
Index.
