  We consider a Fermi gas at unitarity trapped by a highly elongated harmonic
potential and solve the equations of two fluid hydrodynamics at finite
temperature. The propagation of sound waves as well as the discretized
solutions in the presence of weak axial trapping are considered. The relevant
thermodynamic functions entering the hydrodynamic equations are discussed in
the superfluid and normal regimes in terms of universal scaling functions. Both
first sound and second sound solutions are calculated as a function of
temperature and the role of the superfluid density is explicitly pointed out.
The density fluctuations in the second sound wave are found to be large enough
to be measured as a consequence of the finite thermal expansion coefficient of
the gas. Emphasis is given to the comparison with recent experimental data.
