  Using Landau's theory of two-fluid hydrodynamics, we investigate first and
second sound propagating in a two-dimensional Bose gas. We study the
temperature and interaction dependence of both sound modes and show that their
behaviour exhibits a deep qualitative change as the gas evolves from the weakly
interacting to the strongly interacting regime. Special emphasis is given to
the jump of both sounds at the Berezinskii-Kosterlitz-Thouless transition,
caused by the discontinuity of the superfluid density. We find that the
excitation of second sound through a density perturbation becomes weaker and
weaker as the interaction strength increases as a consequence of the decrease
of the thermal expansion coefficient. Our results can be relevant for future
experiments on the propagation of sound in the BEC side of the BCS-BEC
crossover of a 2D superfluid Fermi gas.
