A perturbation theory for acoustoelastic effects is expressed in two sets of coordinates referring to an elastic medium before or after the application of a static stress. The relation between the two corresponding definitions of the phase shift is derived and expressed in terms of energy densities of the unperturbed wave field. This relation generalizes a well-known one, limited to homogeneous and isotropic cases, and allows converting the natural into the true velocity change with little restriction on the medium and type of wave. Examples include bulk waves in anisotropic media and Rayleigh waves in a heterogeneously loaded half-space.