Observation of a second-sound-like mode in superfluid-filled aerogel

Superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is interesting acoustically because it can support more than one mode of sound propagation, and these can be used to study critical properties. Recently, there has been interest in superfluid-filled aerogels, but for such compressible materials one does not observe the ordinary (fourth) sound; instead there is a mode intermediate between first and fourth sound and a second-sound-like mode. We present a theory for the modes and the first observation of the aerogel second-sound-like mode, which is important because it propagates near the critical temperature.