Pulse Shapes of Spherical Waves Reflected and Refracted at a Plane Interface Separating Two Homogeneous Fluids

Abstract

A review is given of Cagniard's method for determining the shapes of the reflected and transmitted waves resulting from a point source of spherical waves of arbitrary waveform located in one of two homogeneous fluids separated by a plane interface. Symmetry relations enable the basic Cagniard solutions for reflection to be obtained from those or transmission, and a reciprocity relation shows that the formulas for transmission when the source is located in one of the two fluids can easily be obtained from the formulas for transmission when the source is located in the other fluid. An Appendix lists explicit solutions for all cases (reflection or transmission with the source located in the fluid of higher or lower soundvelocity). The propagation of jump discontinuities the Cagniard solution is shown to be in agreement with geometrical ray theory. Impulse reflection and transmission coefficients are obtained from the asymptotic values of the basic Cagniard solutions. It is then demonstrated that these same coefficients can be deduced from a solution to Laplace's equation.