The large number of text books on the theory of sound deal principally with periodic disturbances such as harmonic wave trains and standing waves and give scant attention to aperiodic disturbances with clearly defined fronts, conveniently called sound pulses. This monograph attempts to fill this gap by providing an up-to-date description of the theory of sound pulses and its developments. The treatment is based on the thoery of linear partial differential equations of hyperbolic type - a method which is frequently simpler and more effective than the commoner one of resolving the pulse into…mehr
The large number of text books on the theory of sound deal principally with periodic disturbances such as harmonic wave trains and standing waves and give scant attention to aperiodic disturbances with clearly defined fronts, conveniently called sound pulses. This monograph attempts to fill this gap by providing an up-to-date description of the theory of sound pulses and its developments. The treatment is based on the thoery of linear partial differential equations of hyperbolic type - a method which is frequently simpler and more effective than the commoner one of resolving the pulse into harmonic components by Fourier analysis; this is especially true of any treatment of pulse fronts as wave fronts in the sense of geometrical optics. The individual chapters deal with the equations of motion, wave fronts and characteristics, geometrical acoustics and their application to reflection problems and the diffraction of a pulse by a wedge, circular cylinder, sphere and other objects. The book will also be of interest to readers concerned with other aspects of wave propagation, such as electromagnetic waves.
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.
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.
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