The assumption of dynamic similarity is used to determine the velocity potential of an unsteady line source which lies on a plane separating two media of different density and sound velocity. The solution first derived is for a source whose strength varies with time as a step function; the pressure in this case may be identified with Hadamard's elementary solution which in a homogeneous fluid is (c/2π) (c2t2-r2)−½ if r < ct, and 0 if r > ct. We next derive the solution for a source whose strength has a delta-function time dependence; we then describe the results for a supersonic point source moving on the interface, and finally we transfer the results to solve the corresponding electromagnetic problem.