In a modern plasma etching device, the plasma sheath potential is usually superposed by an externally driven oscillating voltage to enhance and control the bombarding ion energy. A collisionless particle simulation is used to study the variation of average kinetic energy < K >(nu(rf)) of bombarding ions as a function of a wide range of sheath oscillation frequency nu(rf) (0.1 nu(pi)less than or equal to nu(rf)less than or equal to 10 nu(pi), where nu(pi) is the ion plasma frequency). It is found that a resonance phenomenon between the ion transit motion and the sheath oscillation can yield a strongly peaked enhancement of < K >(nu(rf)) near nu(rf)similar or equal to 0.5 nu(pi). Ion species with different mass show the peaks at different nu(rf). The relative importance of different ion molecules in an ion-enhanced etching process will be sensitive to nu(rf). This phenomenon may allow a reduction of the undesirable capacitive coupling by optimizing nu(rf) to yield an enhanced < K > of desired ion species at low applied voltages.