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In this paper some of the experimental considerations for obtaining phonon attenuation in solids by Brillouin scattering are described. Measurements of room temperature damping of longitudinal hypersonic waves in α-quartz, fused silica, and calcium fluoride are reported. The observed phonon frequency and linewidth for backward scattering of 6328-Å light in these solids is typically ∼ 30 GHz and ∼ 30 MHz (FWHM), respectively. This corresponds to a damping length of , which is inaccessible by conventional ultrasonics techniques.