## Abstract

In this paper the problem of interaction between infinitesimal disturbances propagated in a fluid and in an elastic solid across an infinite plane interface is examined by the method of dynamic similarity. The disturbance is the result of the setting up, at time t = 0, of an infinite line source of constant strength on the interface; by the word source we imply within the fluid a line singularity associated with a flux which is uniform in all directions and with zero circulation. Seen from the solid the singularity is a line of pressure which is not, however, uniform in all directions. There are three propagation velocities involved, the velocity of sound in the fluid and the velocities of shear and dilatation waves in the solid. The form of the disturbance depends on the relative magnitudes of these velocities, as well as on the relative densities of the two media. Within the limitations of the theory of propagation of weak shocks, the method of dynamic similarity, which is closely related to the conical flow method of Busemann leads to exact formulae for the stress and velocity components everywhere; these results satisfy the correct continuity conditions at the interface. The non-uniform way in which the solution approaches the corresponding elastic half-space solution when the density of the fluid is small relative to that of the solid is described, and the non-uniform way in which the surface wave velocity is affected by the relative density is also discussed. Specific results which are found are that a pair of lines of stagnation move away from the source in opposite directions on the interface with the exact velocity of the Rayleigh wave for the solid. There is another pair of stagnation lines moving with velocity 2$^\frac{1}{2}$c$_2$, where c$_2$ is the velocity of shear waves, but only in cases when this velocity is smaller than the sound velocity in the fluid.