The authors theoretically investigate the manifestations of the non-monotonic character and anisotropic peculiarities of the correlation functions of the inhomogeneities in the dispersion law and damping of plasma waves. The following specific effects have been found: a change in the character of the modifications, dispersion law and damping for small wavenumbers; dependence of the plasma frequency shift on the direction of the wave propagation. They substantiate possibilities for developing the correlation spectroscopy of plasma waves which would enable them not only to measure a correlation radius of the inhomogeneities (this has been suggested earlier), but also to obtain information in the form of the correlation function.