Relation of the Exact Transient Solution for a Line Source near an Interface between Two Fluids to Geometrical Acoustics

The exact transient solution obtained by the Lamb‐Cagniard‐Smirnov‐Sobolev‐Pekeris method is summarized for waves from a line source of arbitrary time dependence near an interface between two fluids of different sound speeds and densities. The solution is used to give an alternate derivation of the pressure (or dp/dt for the refracted arrival wave) increments at times of onset of the reflected, refracted arrival, and transmitted waves originally obtained by the geometrical acoustics theory of Friedrichs and Keller for incident weak shocks. The exact theory shows that the Friedrichs‐Keller results (rigorously valid at onset times) may be extended to give an asymptotic approximation for waveforms following onset times. The strength of the logarithmic singularity accompanying the refracted arrival wave when the incident pressure is discontinuous is also derived from the exact theory.