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Superfluid component is accelerated by gradients in the chemical potential of the liquid [1]. The acceleration is given by \[ \frac{ \partial v_s}{\partial t}=-\nabla \mu=-\frac{\nabla p}{\rho}+s\nabla T\]  When taking thermal motions into account in a fluid, a pressure term comes into play and the net mass current is accelerated by the gradient in this pressure and is related by \[\frac{ \partial}{\partial t} (\rho_sv_s+\rho_nv_n)=\nabla p\]   Further linearizing the density, pressure, and temperature give rise to phase velocities of two sound modes \[ \left( 1-\frac{c^2}{c_1^2}\right) \left(1-\frac{c^2}{c_2^2}\right)=1-\frac{C_p}{C_v} \]  $C_p=T(\partial $C_p=T\frac{\partial  s}{\partial T}_p$ and $C_v=T\frac{\partial s}{\partial T}_v$ are specific heats. The $c_1$ and $c_2$ are the phase velocities of first and second sound respectively given by $c_1^2=(\partial p}{\partial \rho)_s$ and $c_2^2=\frac{\rho_s T s^2}{\rho_n C_p}$ and these are two of the sounds investigated in the lab.