A plane elastic wave propagating in a piezoelectric crystal may be accompanied by longitudinal electric fields which provide an additional elastic stiffness. When the crystal is also semiconducting, these fields produce currents and space charge resulting in acoustic dispersion and loss. A linear theory of this effect is developed, taking into account drift, diffusion, and trapping of carriers for both extrinsic and intrinsic semiconductors. Conductivity modulation sets an upper limit on strain amplitude for a linear theory. The directional characteristics and the magnitude of the effects are illustrated for CdS and GaAs. The Appendix treats the interaction of an arbitrary acoustic plane wave with the electromagnetic fields in a piezoelectric crystal (based on a treatment by Kyame [J. J. Kyame, J. Acoust. Soc. Am.21, 159 (1949);26, 990 (1954).]) and further shows explicitly that only the effects of longitudinal electric fields need be considered.