Hydrodynamic modes in dense trapped ultracold gases

We consider the hydrodynamic modes for dense trapped ultracold gases, where the interparticle distance is comparable to the scattering length. We show that the experimental determination of the hydrodynamic mode frequencies allows one to obtain quite directly the equation of state of a dense gas. As an example, we investigate the case of two equal fermionic populations in different hyperfine states with attractive interaction.