A theoretical study is performed of the bulk acoustic wave propagation in periodic piezoelectric structures with metallized interperiod boundaries. A crucial specific feature of such structures is that the bounded acoustic beam incident perpendicular to an interface can generate scattered (i.e. reflected and transmitted) waves over the whole area of the interface rather than only within the spot where this acoustic beam crosses the interface as it occurs in the absence of metallization. This extra generation is due to the electric potential which is induced by the incident wave on the whole metallized boundary rather than only on its part. The expressions are obtained for the reflection and transmission coefficients in the case where a longitudinal wave propagates along the 6-fold symmetry axis of a hexagonal piezoelectric. The periodicity is realized by inserting thin metallic layers (electrodes) into otherwise homogeneous material perpendicular to its 6-fold axis. The derived expressions allow the determination of the amplitude of waves arising both inside and outside the incident acoustic beam. The analysis of these expressions shows that the extra generation in question is able to significantly alter the distribution of the wave amplitudes as compared with the pattern which is obtained without taking into account the wave fields appearing outside the domain occupied by the incident acoustic beam.