Experimental Determination of the Fourth Sound Velocity in Helium II

Fourth sound is a pressure and density wave in He II, in which only the superfluid is in motion. Using packed rouge to lock the normal fluid, the existence of this wave mode has been experimentally confirmed by measuring the temperature dependence of a plane-wave resonance in a closed-closed cylindrical acoustic resonator. The measured phase velocity has a temperature dependence which agrees within 1% with that predicted theoretically. Pulse measurements using 40-kc/sec sine-wave bursts further corroborate the existence of this type of wave. The absolute value of the fourth sound velocity is affected by the coherent multiple scattering of the wave from the superleak material. The results of Twersky's and Saxon's scattering theories are compared with the data. It is found that the equation n= (2-P) ^1{2}, where n is the index of refraction and P is the porosity, fits the data within 3%. Values of the ratio of the superfluid to the He II density, derived from the fourth-sound data, agree within 2% with those obtained by other experimental techniques.