How Does Phonon Contribution Affect Heat Capacity in Liquid Helium Below 0.6K?

[precondition]

Below 0.6K the heat capacity of liquid He is well represented by the equation
Cv=(9.819 x 10^-3 K^-3)NkT^3
Given that transverse shear waves cannot propagate in a liquid, predict the phonon contribution to the heat capacity of He from the data
c=238 m/s (speed of sound in liquid He)
p=0.145 g cm^-3 (density of liquid He)

......difficult...T_T

 

[precondition]

x is supposed to be multiplication
N number of molecules
k Boltzmann's constant
T temperature in kelvin
Cv heat capacity

 

[StatMechGuy]

I find this rather hard to follow since I'm not getting that the specific heat has a T^3 dependence at low temperatures for a system of massless bosons (read: the phonons). I'm getting that U ~ T^3 and, then C_v ~ T^2, so I'm a little confused. I also haven't slept much the past two weeks so I could be doing something silly here.