Particle image velocimetry (PIV) measurements and flow visualization in a water tunnel show that vortex shedding at the leading and trailing edges of rectangular cylinders can be simultaneously phase-locked to transverse velocity perturbations when the applied perturbation Stp is close to an impinging leading-edge vortex/trailing-edge vortex shedding (ILEV/TEVS) frequency. The transverse perturbations, analogous to β-mode duct acoustic resonances, are generated through harmonic oscillations of the sidewalls. When this occurs, the leading-edge vortices are found always to pass the trailing edge at the same phase in the perturbation cycle regardless of the chord-to-thickness (c/t) ratio. Applying perturbations at an Stp not equal to the natural global frequency also results in phase-locked vortex shedding from the leading edge, and a near wake with a frequency equal to the perturbation frequency. This is consistent with previous experimental findings. However, vortex shedding at the trailing edge is either weaker or non-existent. PIV results and flow visualization showed trailing-edge vortex growth was weaker because leading-edge vortices arrive at the trailing edge at a phase in the perturbation cycle where they interfere with trailing-edge shedding. The frequencies at which trailing-edge vortices form for different c/t ratios correspond to the natural ILEV/TEVS frequencies. As in the case of natural shedding, peaks in base suction occur when the leading-edge vortices pass the trailing edge at the phase in the perturbation cycle (and thus in the leading-edge shedding cycle) that allows strong trailing-edge shedding. This is the reason for the similarity in the Stvs.c/t relationship for three seemingly different sets of experiments.