Superfluid Helmholtz Resonators

It is shown that the master equation for a superfluid Helmholtz resonator is ${\omega }^2=\frac{{u_n}^{2}A}{\mathrm{LV}}$, where $\omega$ is the angular-resonant frequency, $u_n$ is alternately the velocity of first, second, and fourth sound, $A$ is the cross-sectional area of the neck of length $L$, and $V$ is the volume of the resonator. The fourth-sound resonance occurs when the resonator is packed with a porous medium which locks the normal fluid component. Experimental results on such a resonator are in agreement with this result.