The two RHIC rings have independent rf systems to accommodate different species. Thus, the radio frequencies can differ when the phase and radial loops are closed, and the rf frequencies of the two rings are not synchronized. A radio frequency difference leads to longitudinally moving beam crossing points. When the crossing points are between the beam splitting dipoles, the beams experience the beam‐beam interaction. Outside the interaction region the beam‐beam interaction is switched off. In this way the tune is modulated. A computation of the tune modulation depth, pulse shape and frequency is presented. Tune modulation measurements are shown. © 2003 American Institute of Physics