An analysis of the propagation of the mean or average plane wave in a compressible isotropic turbulent plasma is presented. It is shown that the average wave separates into a longitudinal and a transverse mode, and their dispersion relations are derived. The analysis is based on the first-order smoothing theory in the form developed by Keller and assuming a Gaussian correlation function. It is found that mode coupling is a strong effect in the short correlation length region but becomes negligible for long correlation lengths. Useful approximations to the dispersion relations are also given for the short, intermediate, and long correlation length regions as well as numerical results for the perturbed propagation constant of the average transverse wave. The application of the theory to a random dielectric medium is pointed out and a quantitative evaluation of the importance of the depolarization term, i.e. the grad div term, in the vector Helmholtz equation is made.