Resonant Mode Conversion of the Second Sound to the First Sound in Liquid Helium II

Abstract

The experimentally observed disappearance below T = 0.5K of the second sound in liquid He II as a separate wave mode and its subsequent propagation at the speed of the first sound (Peshkov [3]) may be interpreted as a resonant mode conversion of the second sound to the first sound. Near the resonant mode coupling point T = T*, where the frequencies of the two waves become equal, the anomalous effect of entropy changes on the first sound and density changes on the second sound, though generally small, become significant. This leads to the resonant mode coupling of the first sound and the second sound and forces them to lose their identities and hence pave the way for the resonant mode conversion of the second sound to the first sound. We give a theoretical framework for this proposition and an estimate for the fraction of the second sound that is mode-converted to the first sound.