  We investigate the propagation of density and temperature waves in a
cylindrically trapped gas with radial harmonic confinement. Starting from
two-fluid hydrodynamic theory we derive effective 1D equations for the chemical
potential and the temperature which explicitly account for the effects of
viscosity and thermal conductivity. Differently from quantum fluids confined by
rigid walls, the harmonic confinement allows for the propagation of both first
and second sound in the long wave length limit. We provide quantitative
predictions for the two sound velocities of a superfluid Fermi gas at
unitarity. For shorter wave-lengths we discover a new surprising class of
excitations continuously spread over a finite interval of frequencies. This
results in a non-dissipative damping in the response function which is
analytically calculated in the limiting case of a classical ideal gas.
