Localization of Third Sound by a Disordered Substrate

We propose the use of third sound in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films on a disordered substrate as a system for the study of Anderson localization in two dimensions. Quantitative predictions for the localization length are made with use of the self-consistent diagrammatic theory of localization. Dramatic effects are predicted in an experimentally accessible regime.