We deal with the wave equation with assigned moving boundary (0 < x < a(t)) upon which DirichletNeuman boundary conditions are satisfied, here a(t) is assumed to move slower than light and periodically. We give a feedback which guarantees the exponential decay of the energy. The proof relies on a reduction theorem by Ammari et al. (2017) [1] and Yoccoz (1984) [13]. At the end we give a remark on the moving-pointwise stabilization problem. (C) 2017 European Control Association. Published by Elsevier Ltd. All rights reserved.