  We calculate the in-plane modes of the vortex lattice in a rotating Bose
condensate from the Thomas-Fermi to the mean-field quantum Hall regimes. The
Tkachenko mode frequency goes from linear in the wavevector, $k$, for lattice
rotational velocities, $\Omega$, much smaller than the lowest sound wave
frequency in a finite system, to quadratic in $k$ in the opposite limit. The
system also supports an inertial mode of frequency $\ge 2\Omega$. The
calculated frequencies are in good agreement with recent observations of
Tkachenko modes at JILA, and provide evidence for the decrease in the shear
modulus of the vortex lattice at rapid rotation.
