The displacement autocorrelation function and its Fourier transform of a substitutional impurity atom in a crystal lattice are calculated for a specific model of a crystal taking into account the change in force constants as well as the change in mass. The results are expressed in terms of the frequency spectrum of the pure crystal and the perturbation parameters characterizing the effect of the impurity. As an application of the calculations the Mössbauer one-phonon absorption cross section is calculated by supposing that only the impurity is Mössbauer-active. Particular attention is paid to the case in which a sharp resonant mode appears in the low frequency region. Using the Debye model, a simple expression is obtained for the ratio of the peak value of the one-phonon line to that of the zero-phonon line.