With recent development in micromachining and energy harvesting techniques, it has become possible to realize self powered autonomous wireless sensors. To effectively scavenge ambient energy, design of the harvester needs to be carefully optimized. In several scenarios kinetic energy is distributed in few harmonics of low frequency oscillations and one has to choose the harmonic to which the harvester has to be tuned. This paper analytically investigates dependence of average power of a vibration energy harvester on frequency of vibration. The role of damping has been carefully considered to reach unambiguous conclusions. It has been shown that, when the magnitude of base acceleration is constant, contrary to what has been claimed, a high frequency harmonic will give more power density than a low frequency one. Cubic dependence of average power on the frequency of vibration holds only when electromechanical coupling coefficient can be increased with frequency. For a constant electromechanical coupling coefficient, power increases with the fourth power of the driving frequency. © 2011 IEEE.