part of the density response function divided by the frequency ω . In studies of superfluid $^{4}$He, this factor of 1 /ω is crucial to probing second sound since, although only weakly coupled to density, the speed of second sound is small and hence, its weight in Brillouin light scattering can be significant. As noted in section II, a similar situation arises in studies of pulse propagation in dilute gases, albeit for very different reasons. In this situation [see (6)], the amplitude of the density pulse induced by a localized (in time and space) density perturbation is proportional to Im χ$_{nn}$ ( q, ω ) /ω . The factor of 1 /ω here results not from the detailed balance factor, but from the Fourier transform of the step-function used to model the time dependence of the perturbing laser beams. Arahata and Nikuni [10] calculated the effect of producing a density fluctuation by a sudden perturbation in a superfluid Fermi gas at unitarity. The final result was two pulses moving with the speeds of first and second sound, with relative amplitudes given by W$_{i}$ as defined in (20). In section III, we showed that the relative weights in S ( q, ω ) and Im χ$_{nn}$ ( q, ω ) of first and second sound are given by W$_{i}$ = Z$_{i}$/u 2 i and B$_{i}$ = Z$_{i}$/u$_{i}$ , respectively, where Z$_{i}$ is defined in (18). These results are valid for any type of superfluid, including weakly interacting atomic Bose gases and also strongly interacting Fermi gases. In this section, we concentrate on strongly interacting Fermi gases where, as discussed above, the thermal expansion is rela- tively small, meaning that density and temperature fluctuations are not strongly coupled. Using the exact relations in (14), in this section we will show that to a very good approx- imation, W$_{2}$/W$_{1}$ is given by (30) in this situation. In section V, we give a brief discussion of the dynamic structure factor in a dilute Bose gas, where the thermal expansion can be much larger when the s -wave scattering length is small. Solving the coupled equations in (14), one obtains the expansions [14, 15] in terms of the parameter defined by x ≡ v $^{2}$/γv2 ¯ $_{s}$. These results show that to lowest order in the parameter x ( γ − 1) ≡ xϵ$_{LP}$ , the first and second sound velocities are well approximated IV. SUPERFLUIDS WITH SMALL THERMAL EXPANSION 11 u 2 1 = v 2 ¯ $_{s}$[1 + ( γ − 1) x + · · · ] , u 2 = v 2 γ [1 − ( γ − 1) x + · · · ] , (24)