An analytic solution is presented for shear motions in a binary mixture of a chemically inert, isothermal, elastic isotropic solid and elastic fluid subject to a sinusoidally varying solid displacement on one boundary and free of tractions on the other. It is demonstrated that the retention of inertial terms, and the resulting resonance phenomenon, can cause solid displacements in the interior of the region orders of magnitude greater than the exciting solid displacement on the boundary. Displacement spectra are presented for certain well known porous media.