The frequency characteristics of spherical photon density waves excited in media with different degrees of scattering anisotropy are studied. Statistical modeling of the frequency and phase responses of the spatial irradiance of the light field emitted by a point-sized isotropic source were performed employing the Monte Carlo technique. The scattering anisotropy of the medium was determined by the Henyey-Greenstein phase function with different values of the mean scattering cosine. It is shown that the scattering anisotropy factor determines the frequency range, in which the effect of the photon path length distribution on the magnitude of the photon density wave dispersion is maximal. In media with quasi-isotropic scattering, dispersion effects are manifested at lower frequencies as compared to those for anisotropic media. The simulation results are compared with the analytical solution for the asymptotic regime of the light field in an isotropically scattering medium.