Experiments on the propagation of sound waves in fused silica glass (Suprasil W) below 1K have been carried out to test theories of the glassy state. The tunneling state model1,2postulates the the existence of a broad distribution of two‐level systems in all glasses which are capable of resonantly scattering phonons, thus accounting for the low phonon thermal conductivities of amorphous dielectrics. Additionally, this model predicts the temperature and frequency dependence of the reciprocal decay length, or absorption, of a phonon:1,3