  We study elementary low energy excitations inside a supersolid. We find that
the coupling between the longitudinal lattice vibration mode and the superfluid
mode leads to two longitudinal modes (one upper branch and one lower branch)
inside the supersolid, while the transverse modes in the supersolid stay the
same as those inside a normal solid. We also work out various experimental
signatures of these novel elementary excitations by evaluating the Debye-Waller
factor, density-density correlation, vortex loop-vertex loop interactions,
specific heat and excess entropy from the vacancies per mole.
