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In addition to conventional applications of ferroelectric crystals that exhibit piezoactivity, such crystals find wide application in the production of domain electronic devices based on the interaction between acoustic waves and ferroelectric domains (acousto-domain interaction) [Esayan et al, 1974]. In the course of the general development of technology of phonon crystals the ferroelectric with periodic domain structures (PDSs) have attracted a considerable interest recently [Golenishchev-Kutuzov et al, 2003]. The interest in such structures with periodically varying elastic, electric, and other physical parameters dates back to the 1960s since, by that time, the possibilities offered by single-domain crystals in the realization of the spectral characteristics of elastic and electromagnetic waves had been exhausted. First of all a ferroelectrics with PDSs differ from usual phonon crystals by ability of its reorganization under external action due to rather fast moving domain walls(DW) [Golenishchev-Kutuzov et al, 2003]. The spectra of elastic oscillations of a ferroelectric with a static PDS may significantly differ from the spectra of a conventional single-domain sample [Li, et al, 1991; Lyubimov & Sannikov, 1979]. This difference is primarily manifested in the formation of forbidden and allowed bands, which are absent in the continuous spectrum of waves in a single-domain crystal. To the full this conclusion extends to oscillation modes of localized at DWs, in particular – to electroacoustic interfacial waves (EIWs) [Maerfield & Tournois, 1971], which were widely studied in ferroelectrics with static PDSs, representing a superlattice [Li, et al, 1991; Nougaoui, 1987]. Considerable modification of spectral parameters of EIWs in superlattices such as boundary localization of oscillation and phase speed was explained in [Lyubimov & Sannikov, 1979; Li, 1987] as result of interaction between electrosound oscillations of neighbo(u)ring DW. At an early stage of research the possibility of the realization of PDSs with various periods of the lattices of domain walls and the possibility of vary lattice period [GolenishchevKutuzov et al, 2003] have shown the prospects of application of the domain superlattices. It was found out, in particular, that crystals with PDSs are effective as broadband piezoconverters of acoustic waves, and with the greater efficiency of transformation, than have monodomain crystals [Batanova & Golenishchev-Kutuzov, 1997]. Other fields of application (the acoustic spectroscopy of polydomain ferroelectrics and processing of the

Electroacoustic Waves in a Ferroelectric Crystal with of a Moving System of Domain Walls