  Using the coarse grain averaged hydrodynamic approach, we calculate the
excitation spectrum of vortex lattices sustained in rotating Bose-Einstein
condensates. The spectrum gives the frequencies of the common-mode longitudinal
waves in the hydrodynamic regime, including those of the higher-order
compressional modes. Reasonable agreement with the measurements taken in a
recent JILA experiment is found, suggesting that one of the longitudinal modes
reported in the experiment is likely to be the $n=2$, $m=0$ mode.
