Sound Pulses (Paperback)

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.