Rarefaction wave velocities have been used to estimate sound velocities on the Hugoniot for a quartz rock and for a perthitic feldspar. The Hugoniot states and rarefaction wave velocities were determined with multiple manganin stress gages placed between successive slabs of the sample material. Hugoniot stress states were produced by impact from explosively driven flyer plates. The sound velocity was determined from the transit time across gage planes of the initial characteristic of the rarefaction wave originating at the flyer plate free surface. Sound velocities (referred to Eulerian coordinates) measured in quartzite was 7.6, 8.1, and 10.5 mm/μs at Hugoniot stresses of 220, 250, and 355 kbar, respectively. Sound velocities measured in feldspar were 7.4, 8.7, and 9.2 mm/μs at Hugoniot stresses of 255, 345, and 460 kbar, respectively. These velocities are close to estimated bulk velocities and imply an almost complete loss of material strength behind the shock front. On the basis of our measured sound velocities and earlier observations by others we suggest that the Hugoniot yielding phenomenon is an adiabatic shear process resulting in partial melting behind the shock front. We further suggest that inhomogeneity in the adiabatic shear process may account for many details of the nonequilibrium mixed phase Hugoniot observed in silicates.