We have used a picosecond optical technique to measure the attenuation {alpha} of longitudinal-acoustic phonons in several disordered solids. We find a universal {alpha}{approximately}{nu}{sup 2} behavior for frequencies {nu} up to 320 GHz and for temperatures between 80 and 300 K. Within this temperature range the phonon attenuation increases by a factor of between 2 and 3 with increasing temperature for the amorphous polymers poly(methyl methacrylate), poly(styrene), and poly(ethyl methacrylate), and for the metallic glass TiNi. We discuss our results in relation to current theories of high-frequency vibrations in glasses and thermal conduction. {copyright} {ital 1996 The American Physical Society.}