The propagation of waves and the flow of fluids through random media are important areas of research not only because they are involved in many practical applications, but also because they exhibit novel phenomena currently under intense investigation in condensed matter physics. Practical applications include acoustic geophysical survey, medical imaging, testing of new composite and porous materials, solar collector design, etc. Modern physical phenomena which are involved include percolation, fractional dimension structures, and Anderson localization. The basic physics underlying wave propagation and flow in random media will be experimentally studied using an ideal liquid, superfluid helium, permeating a random system. In particular, fourth sound propagating in various random porous media and third sound in a superfluid film on a random substrate will be investigated.