Porosity dependence of sound propagation in liquid ${}^4$He filled aerogel

Longitudinal sound wave propagation has been studied in an aerogel-liquid ${}^4$He system for various porosities of aerogel. The superfluid transition was identified as the absorption peak, whose magnitude was suppressed by aerogel. The sound velocity was analyzed within a hydrodynamic theory in both normal and superfluid phases. The absorption peak due to phonon-roton interaction around 1 K was not observed even with the most porous aerogel. The low temperature sound velocity and attenuation show that direct collisions of phonons with aerogel strands plays an important role in the acoustic properties.