  Using a variational approach, we solve the equations of two-fluid
hydrodynamics for a uniform and trapped Fermi gas at unitarity. In the uniform
case, we find that the first and second sound modes are remarkably similar to
those in superfluid Helium, a consequence of strong interactions. In the
presence of harmonic trapping, first and second sound become degenerate at
certain temperatures. At these points, second sound hybridizes with first sound
and is strongly coupled with density fluctuations, giving a promising way of
observing second sound. We also discuss the possibility of exciting second
sound by generating local heat perturbations.
