We discuss the interaction of an externally generated ultrasonic wave with a thin magnetic film, and the generation of phonons by driving such a film with a microwave field. Several geometries are considered. If the frequency of the driving wave is close to one of the spin-wave resonance frequencies of the film, we exhibit an exact solution to the phonon equation of motion in the presence of one-magnon-one-phonon terms in the magneto-elastic coupling. Some difficulties present in an earlier theory are eliminated. We find a contribution to the spin wave resonance linewidths from the one-magnon-one-phonon terms. For the n=0 term of a Ni film, we estimate the magneto-elastic coupling may make a contribution to the linewidth of roughly ten percent of the total linewidth. If we denote this contribution to the linewidth by Γn(pn) and the total linewidth by Γn, then we show that study of the interaction of an externally generated ultrasonic wave with the film provides a direct measure of the ratio Γn(pn)Γn. The presence of a poor acoustical impedance match at a film surface is shown to introduce a factor in the expression for Γn(pn) periodic in the external magnetic field, for a film of fixed thickness.