GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s54> GLYPH<s48>GLYPH<s46>GLYPH<s56> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s51> GLYPH<s48>GLYPH<s46>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s54> GLYPH<s115>GLYPH<s101> GLYPH<s99> GLYPH<s111> GLYPH<s110> GLYPH<s100> GLYPH<s32>GLYPH<s115>GLYPH<s111> GLYPH<s117> GLYPH<s110> GLYPH<s100> GLYPH<s83>GLYPH<s111>GLYPH<s117>GLYPH<s110>GLYPH<s100>GLYPH<s32>GLYPH<s118>GLYPH<s101>GLYPH<s108>GLYPH<s111>GLYPH<s99>GLYPH<s105>GLYPH<s116>GLYPH<s105>GLYPH<s101>GLYPH<s115>GLYPH<s32>GLYPH<s91>GLYPH<s105>GLYPH<s110>GLYPH<s32>GLYPH<s117>GLYPH<s110>GLYPH<s105>GLYPH<s116>GLYPH<s115>GLYPH<s32>GLYPH<s111>GLYPH<s102>GLYPH<s32> GLYPH<s118> GLYPH<s70> GLYPH<s93> GLYPH<s84> GLYPH<s47> GLYPH<s84> GLYPH<s67> GLYPH<s102> GLYPH<s105> GLYPH<s114>GLYPH<s115>GLYPH<s116>GLYPH<s32>GLYPH<s115>GLYPH<s111> GLYPH<s117> GLYPH<s110> GLYPH<s100> FIG. 1: Speeds of first and second sound in a unitary superfluid Fermi gas. The dashed lines are the approximations c$_{1}$ = v$_{¯}$ s and c$_{2}$ = v/ √ γ , as given by the leading terms in (24) (from [8]). by In figure 1, we show the temperature dependence of u$_{1}$ and u$_{2}$ and compare these results with the leading order expressions c$_{1}$ and c$_{2}$ given by (25) (shown by the dashed lines). The thermodynamic functions needed to obtain these sound speeds are calculated using the microscopic theory of Nozi` eres and Schmitt-Rink (NSR) [25, 26]. We see that c$_{1}$ and c$_{2}$ are extremely good approximations at all temperatures. At temperatures T ≳ 0 . 4 T$_{c}$ , x = c 2 $_{2}$/c 2 1 is very small, even though ϵ$_{LP}$ ∼ O (1). At lower temperatures, while x is no longer small ( x = 1 / 3 at T = 0), ϵ$_{LP}$ becomes extremely small. Thus in both limits, we find that the correction term xϵ$_{LP}$ in (24) is negligible. The fact that u$_{1}$ ≃ c$_{1}$ and u$_{2}$ ≃ c$_{2}$ in a fluid with small thermal expansion such as the uni- tary Fermi gas means that first and second sound propagate at essentially the same velocities as pure density and temperature oscillations, as would arise when ϵ$_{LP}$ = 0. Surprisingly, this does not mean that first and second sound are uncoupled density and temperature oscillations. We discuss this in detail in B. 12 c 2 1 = v 2 ¯ $_{s}$, c 2 = v 2 γ = T ¯ s 2 0 ¯ c$_{p}$ ρ$_{s}$$_{0}$ ρ$_{n}$$_{0}$ . (25)