  Second sound is an entropy wave which propagates in the superfluid component
of a quantum liquid. Because it is an entropy wave, it probes the thermodynamic
properties of the quantum liquid which are determined, e.g., by the interaction
strength between the particles of the quantum liquid and their temperature.
Here, we study second sound propagation for a large range of interaction
strengths within the crossover between a Bose-Einstein condensate (BEC) and the
Bardeen-Cooper-Schrieffer (BCS) superfluid. In particular, we investigate the
strongly-interacting regime where currently theoretical predictions only exist
in terms of an interpolation between the BEC, BCS and unitary regimes. Working
with a quantum gas of ultracold fermionic $^6$Li atoms with tunable
interactions, we show that the second sound speed varies only slightly in the
crossover regime. We gain deeper insights into sound propagation and excitation
of second sound by varying the excitation procedure which ranges from a sudden
force pulse to a gentle heating pulse at the cloud center. These measurements
are accompanied by classical-field simulations which help with the
interpretation of the experimental data. Furthermore, we determine the spatial
extension of the superfluid phase and estimate the superfluid density. In the
future, this may be used to construct the so far unknown equation of state
throughout the crossover.
