# Calculating first harmonic of second sound

I can't find some of the values I need for this calculation, which I'm trying to do prior to an experiment around superfluidity. Specifically I am trying to get a rough estimate of the first harmonic for second sound in superfluid $^4$He, in a tube 10cm long, at 1.6K. Closed at both ends. Subscript n relates to the normal fluid fraction, s to the superfluid component. The velocity of second sound is given by

$$c = \sqrt{\frac{TS^2\rho_s}{C\rho_n}}$$

Then since $c = f \lambda$ and $\lambda = \frac{L}{2}$,

$$f = \frac{2}{L} \sqrt{\frac{TS^2\rho_s}{C\rho_n}}$$ L, T I know, I can remove $\rho_s$ using $\rho_s v_s + \rho_n v_n = 0$ so that the equation becomes

$$f = \frac{2}{L} \sqrt{-\frac{TS^2v_n}{Cv_s}}$$ But $\frac{-v_n}{v_s}$ will be positive overall since either $v_n$ or $v_s$ will be defined as negative, the superfluid and normal components move in opposite directions I think. So I just need to find the entropy S of Helium 4 at 1.6K and its heat capacity, since I know the velocities of first and second sound at 1.6K, but I can't find those values anywhere. Is there another way to calculate this, or could someone direct me to some tables of constants? I have tried Kaye and Laby, and the internet in general, with no luck.

Most likely my approach is incorrect, although I haven't been able to find an alternative.

• For first harmonic λ/2 = L . which gives λ = 2L . – shrey Jan 25 '17 at 11:46
• @shrey Good point, thanks, thinking of one end open one closed I think. – user13948 Jan 25 '17 at 14:01