The temperature dependence of the attenuation of longitudinal waves propagating along thecaxis of aluminum oxide and ruby has been measured at frequencies of 0.4 GHz, 1.23 GHz, 2.32 GHz, and 2.94 GHz in the temperature range 20° to 100°K. The ruby samples contained 0.025, 0.08, 0.2, and 0.9% chromium by weight. respectively. In undoped aluminum oxide, in the temperature range 40° to 50°K, the attenuation is frequency independent and varies asT9. At higher temperatures, the attenuation is frequency dependent and varies less rapidly with temperature. The effect of chromium impurities is to increase the attenuation at low temperatures and to decrease it at high temperatures. The measurements are interpreted in terms of collisions between the low‐energy phonons, constituting the sound wave, and the thermal phonons. Evidence is presented that the main contribution to the attenuation is from collisions of the sound‐wave phonons with transverse thermal phonons. The dependence of the attenuation on temperature, frequency, and chromium concentration found experimentally is in good agreement with that theoretically predicted for this type of collision mechanism.