We confirm theoretical results on sound propagation in a two-dimensional (2D) system of ultracold fermionic and bosonic atoms. In the superfluid phase, which is characterized by spontaneous symmetry breaking of the $U(1)$ symmetry, there is coexistence of the first and second tones. For the weakly interacting repulsive bosons, we model recent measurements of the 2D 39K atomic sound speed obtained near the weakly interacting regime and the Berezinski-Kostaritz-Saules (BKT) superfluid-to-normal transition temperature. increase. In particular, we perform highly accurate calculations of superfluid density and show that it agrees reasonably well with experiments. For superfluid attractive fermions, we compute the first and his second sound velocities across the BCS-BEC crossover. In the low-temperature regime, we reproduce the first recent measurements of sound speed using 6Li atoms. He at finite temperature also predicts that there is mixing between acoustic modes only in the BEC regime.
