Two-fluid hydrodynamics leads to the coupled equations [2, 3] As noted above (see figure 1), the speeds of first and second sound are well approximated by c$_{1}$ and c$_{2}$ in (25). Physically, this means that to leading order, the pressure fluctuations in first sound are at constant entropy per unit mass ¯ s and hence, δP ≃ ( ∂P/∂ρ )$_{¯}$ $_{s}$δρ . Similarly, the temperature fluctuations in second sound are to leading order at constant pressure and hence, δT ≃ ( ∂T/∂ ¯ s )$_{p}$ δ ¯ s . Using these in (26) leads to the leading order expressions for u$_{1}$ and u$_{2}$ given in (24). We remark that, qualitatively, our results in figure 1 for the temperature dependence of u$_{1}$ and u$_{2}$ are in agreement with Arahata and Nikuni [10], who also based their work on NSR thermodynamics. The differences with [10] at high and low temperatures are easily understood. Direct numerical calculations based on NSR are difficult to do accurately for T < 0 . 4 T$_{c}$ because of the extremely small value of the normal fluid density. Our results in figure 1 in this region are based on the assumption that Goldstone phonons are the dominant thermal excitations at low T at unitarity, which allows us to obtain the low temperature values of u$_{1}$ and u$_{2}$ analytically. In the opposite limit of high temperatures close to T$_{c}$, our calculations show that W$_{2}$ steadily increases, in contrast with that of [10]. For T close to T$_{c}$ , it is crucial to use a superfluid density with the correct critical behaviour [27], removing the spurious first-order behaviour predicted by NSR [28]. (In fact, this behaviour is not unique to NSR and is symptomatic of any theory that treats phase fluctuations in a perturbative way. See [29] for further discussion.) Using the values of u$_{1}$, u$_{2}$ , and v (see figure 1), we can calculate Z$_{2}$, W$_{2}$ and W$_{1}$ . The results are shown in figure 2. The relative weight of second and first sound in S ( q, ω ) is given by Using the exact two-fluid expressions for u$_{1}$ and u$_{2}$ gives the ratio W$_{2}$/W$_{1}$ shown in figure 3. For comparison, we also plot the Landau-Placzek ratio ϵ$_{LP}$ = γ − 1, calculated directly from the same thermodynamic functions used to obtain the sound speeds u$_{1}$ , u$_{2}$ , and v [7, 8]. In figure 4, we plot S ( q, ω ) given by (22). This shows the first and second sound resonances at a series of temperatures. The results shown in figures 2-4 show the remarkable feature that, even though the maximum value of Z$_{2}$ is ∼ 0 . 05 at T ∼ 0 . 8 T$_{c}$ , the relative weights of 13 W$_{2}$ W$_{1}$ = Z$_{2}$u 2 1 Z$_{1}$u 2 = v 2 − u 2 u 2 1 v 2 u 2 1 u 2 . (27) u $^{2}$δρ = δP, u $^{2}$δ ¯ s = ¯ s 2 0 ρ$_{s}$$_{0}$ ρ$_{n}$$_{0}$ δT. (26)