  We study a cross-shaped cavity filled with superfluid $^4$He as a prototype
resonant-mass gravitational wave detector. Using a membrane and a re-entrant
microwave cavity as a sensitive optomechanical transducer, we were able to
observe the thermally excited high-$Q$ acoustic modes of the helium at 20 mK
temperature and achieved a strain sensitivity of $8 \times 10^{-19}$
Hz$^{-1/2}$ to gravitational waves. To facilitate the broadband detection of
continuous gravitational waves, we tune the kilohertz-scale mechanical
resonance frequencies up to 173 Hz/bar by pressurizing the helium. With
reasonable improvements, this architecture will enable the search for GWs in
the 1-30 kHz range, relevant for a number of astrophysical sources both within
and beyond the Standard Model.
