Impure superfluids exhibit very unusual properties including unexpected acoustic features. We calculate the coupling between temperature and pressure oscillations for impure superfluids and for superfluid He in aerogel and show that the coupling between first and second sound modes is governed either by c∂ρ/∂c (c is impurity concentration) or by σρaρs (ρa is aerogel density), rather than by the thermal expansion coefficient ∂ρ/∂T, which is enormously small in pure superfluids. This replacement plays a fundamental role in sound phenomena. It leads to the existence of such phenomena as the slow 'pressure' waves and fast 'temperature' waves and modifies significantly all sound conversion phenomena.
Brusov, P., Brusov, P., Lawes, G., Parpia, J., Lee, C., Matsubara, A., & Ishikawa, O. (2003). Novel sound phenomena in superfluid helium in aerogel and other impure superfluids. Physica B: Condensed Matter, 329-333(1), 329-333. https://doi.org/10.1016/S0921-4526(02)02075-6