We investigate the response of an acousto-optic bistable device to time-varying acoustic inputs. The device modeled by a two-hump one-dimensional autonomous nonlinear map in which the (implied) is justifiably period is determined by the feedback time of the device. Our newly added time-varying input has a map period much greater than the feedback time and for simplicity is taken in the form of a periodic square pulse. We use numerical simulation and a matrix method to predict the general behavior of the output intensity at specific instants of time. Background knowledge, viz., general comments on the nature of one-two-hump one-dimensional maps and their distinction, is also presented in a unified fashion to aid in and the understanding of the dynamics of the device. We find that novel changes of the output period can occur for significant feedback amplitudes, and that these changes can be sensitively controlled.