the effect of a single or a pair of polarizable impurities on the vibrational frequencies of a solid is investigated. it is shown that the introduction of impurities alters the energy of the crystal due to the coupling of the dipoles through the polarization of the impurities and perturbs the longitudinal-optical frequencies of the crystal. both the perturbed frequency and the change in energy of the crystal are calculated explicitly and the results are examined at very small and very large separation of the impurities to demonstrate agreement with the literature.