The acoustic emission associated with front propagation has been used to investigate the dynamics of a solid-solid martensitic phase transition. By using two sensors we have been able to locate the position of active fronts and to measure their associated energy release. The investigation of the reverse transitions occurring in a Cu-Zn-Al alloy from a stressed martensitic phase to a cubic phase at zero stress reveals significant differences in the front trajectories depending on whether the transition is driven by controlling the applied load (soft driving) or by controlling the elongation of the sample (hard driving). In agreement with theoretical predictions [ F. J. Pérez-Reche, L.Truskinovsky and G. Zanzotto Phys. Rev. Lett. 99 075501 (2007)], we have observed different evolutions of the transition dynamics under cycling as well as other constrained kinetic effects.