Transition radiation is investigated from a bunch intersecting a dielectric plate excited by acoustic waves. The latter generate a super lattice the characteristics of which are controlled by tuning the amplitude and the wavelength of the acoustic field. Within the framework of quasiclassical approximation, a formula is given for the spectral and angular distributions of the radiation intensity in the forward direction in the general case of distribution function of electrons in the bunch. The coherence effects are discussed for several special cases of the longitudinal distribution function. It is shown that the presence of the acoustic filed gives rise to new peaks in both the spectral and angular distributions of the radiated energy. The heights and the widths of these peaks are controlled by the thickness of the plate and by the parameters describing the acoustic super lattice.

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