Coupled wave propagation phenomena have been observed in laboratory measurements for a long time; however in field experiments observations have been less convincing. In this paper coupled wave equations allow us to model such coupling by combining elastic stress and strain, electric field strength and displacement, entropy and temperature. For piezoelectric media slowness surfaces show changes in propagation velocity and particle motion when coupling is included in the computation. Average properties of such media can be computed using the Schoenberg and Muir group theory. Possible applications of coupled wave propagation, besides earthquake prediction and mineral exploration, might be the 3D monitoring of oil fields during enhanced oil recovery. Accurate rock parameter estimation seems to be sensitive to coupling effects.