In previous experiments, the vortex-shedding frequency in the flow around rectangular prisms has been found to follow a stepwise variation with chord-to-thickness ratio for two different situations: the natural shedding at low Reynolds number and the excitation of a resonant transverse acoustic mode of a duct for flows at moderate Reynolds numbers. This stepwise variation disappears for natural shedding at Reynolds number higher than approximately 2000; however, it is present at the higher Reynolds numbers for the acoustically perturbed case. The present experimental study shows that if the flow is forced by small transverse oscillations, similar in form to the resonant transverse acoustic mode, the leading-edge and trailing-edge vortex shedding are locked over a wide range of forcing frequencies. However, a stepwise variation in the frequency at which peak base drag occurs is found even at these higher Reynolds numbers. The stepwise frequency variation of vortex shedding in the natural shedding case and the acoustic resonance case are then explained in terms of preference of the flow to shed trailing-edge vortices at peak base drag.