We consider a mathematical model of propagation of weak elastic perturbations in acoustically inhomogeneous solids. The acoustic inhomogeneity and anisotropy of the body are induced by a field of initial strains. A linearized system of dynamic equations obtained for the Murnagan cubic potential of elasticity includes coefficients depending on the components of initial strains. An iterative approach proposed for the solution of this system of equations whose coefficients depend on space coordinates enables us to reduce the problem to the solution of a sequence of inhomogeneous wave equations with constant coefficients. Even in the zero-order approximation, this approach enables us to establish relations connecting the mean phase velocities of plane monochromatic waves of various types with linear integrals of the components of strains for arbitrary directions of propagation of waves. The corresponding relations are presented for the case of plane deformation.