First and second sound speeds are calculated for a uniform superfluid gas of
fermi atoms as a function of temperature, density and interaction strength. The
second sound speed is of particular interest as it is a clear signal of a
superfluid component and it determines the critical temperature. The sound
modes and their dependence on density, scattering length and temperature are
calculated in the BCS, molecular BEC and unitarity limits and a smooth
crossover is extrapolated. It is found that first and second sound undergo
avoided crossing on the BEC side due to mixing. Consequently, they are
detectable at crossover both as density and thermal waves in traps.Comment: To appear in Phys. Rev.