We consider the conversion of first sound into second sound and the reverse in different impure superfluid systems. We calculate the coupling between temperature (entropy) oscillations and pressure (density) oscillations for impure superfluids (including ${}^3\mathrm{He}{-}^4\mathrm{He}$ mixtures) and for superfluid He (both ${}^3\mathrm{He}$ and ${}^4\mathrm{He})$ in aerogel and show that sound conversion in these systems is governed by $c(\partial \rho /\partial c)$ or by $\sigma {\rho }_a{\rho }_s$ (instead of $\partial \rho /\partial T,$ which is enormously small in pure He). This replacement plays a fundamental role in the sound conversion phenomenon in impure superfluids and superfluids in aerogel. It enhances the coupling strengths of the two sounds and decreases the threshold values for nonlinear processes in homogeneous superfluids. Some phenomena such as the slow mode of superfluid ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ in aerogel, and heat pulse propagation with the velocity of first sound in HeII in aerogel can be understood as a double sound conversion phenomena.

• Received 18 September 2000

DOI:https://doi.org/10.1103/PhysRevB.63.140507