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