result that second sound is the dominant excitation in S ( q, ω ) and mainly involves a pure oscillation of the condensate in the presence of a static thermal component [3, 4]. However, first and second sound in a strongly interacting Bose gas are similar to those in a Fermi gas near unitarity (see figure 7). We thank Lev Pitaevskii for useful comments. E.T. was supported by nsf-dmr 0907366 and ARO W911NF-08-1-0338. H.H. and X.-J.L. were supported by ARC and NSFC. S.S. acknowledges the support of the EuroQUAM FerMix program. A.G. was supported by NSERC and CIFAR. At low temperatures, Goldstone phonons determine the thermodynamics of both super- fluid $^{4}$He and Fermi gases. For phonons with velocity c , the free energy F and normal fluid density ρ$_{n}$$_{0}$ are given by [41] (Recall that we have set ℏ = k$_{B}$ = 1) and Using (A1), it is straightforward to show that and In arriving at these expressions, the temperature dependence of the Goldstone phonon ve- locity c has been ignored. P$_{0}$ is the pressure in the ground state. These results can be combined to give 25 ¯ c$_{p}$ = ¯ c$_{v}$ − T ( ∂ ¯ s ∂ρ ) T ( ∂P ∂T ) ρ ( ∂P ∂ρ ) − 1 T = ¯ c$_{v}$ + 4 π $^{4}$T 7 45 $^{2}$ρ$^{2}$c$^{6}$v 2 T [ 1 + 3 ρ c ( ∂c ∂ρ ) T ] 2 , (A6) ¯ c$_{v}$ = 2 π $^{2}$T 3 15 ρc 3 . (A5) P = − ( ∂F ∂V ) T,N = P$_{0}$ + π $^{2}$T 4 90 c 3 [ 1 + 3 ρ c ( ∂c ∂ρ ) T,N ] , (A4) ¯ s$_{0}$ = − 1 mN ( ∂F ∂T ) V,N = 2 π $^{2}$T 3 45 ρc 3 , (A3) ρ$_{n}$$_{0}$ = 2 π $^{2}$T 4 45 c 5 . (A2) F = F$_{0}$ − V π $^{2}$T 4 90 c 3 (A1) Appendix A: Phonon thermodynamics at low temperatures Acknowledgments