The spectral properties of composite materials based on small particles under 1D, 2D, and 3D size confinement are described using a combination of dispersive internal field and effective media theory approaches. Calculations performed for a number of crystalline materials have shown that the peak position and intensity of the vibrational band of the material under conditions of 1D, 2D, and 3D size confinement are changed, whereas the bandwidth of the band remains the same. In the case of 3D confinement, the peak position of the spectrum of isolated "mesoparticles" (epsilon(2)(meso)) appears to be very close to the intrinsic frequency of the lattice vibrations, calculated from the elastic constants of this crystal, as well as to the Frohlich's frequency. The largest shift (Delta nu) of the peak frequency, nu(max), from the bulk value is obtained in the case of 1D confinement when the peak position is practically coincident with the frequency of the longitudinal optical phonon (nu(LO)). These shifts are the result of intermolecular interactions, including both resonant and induced resonant dipole-dipole interactions.