In this paper we are interested in the acoustic scattering by plane periodic media immersed in a fluid. In particular, the effects of viscosity on the stop and pass bands are investigated both theoretically and experimentally. We consider N periods of an elementary cell composed of two plates, presenting a high impedance contrast, with only one being considered viscous. Experimental results demonstrate the influence of the incidence side, and the developed theoretical models validate this phenomenon explicitly. A comparison of theoretical and experimental reflection spectra of a multilayered structure composed of N (2 ≤ N ≤ 5) periods of plane layers is presented in the frequency range from 0.5 to 3.5 MHz. The period consists of two isotropic plates considered as perfectly bonded, one in aluminum (elastic), the other in polyethylene (viscoelastic). Moreover, the influence of the number of periods is discussed. It is shown that the number of periods necessary to obtain stable stop and pass bands depends on the geometrical and physical characteristics of the viscoelastic plate. For the configurations under study, it is demonstrated that three periods ensure the convergence of the reflection spectrum.