We have extended earlier absorption measurements between 500 and 10 000 Mc/sec to temperatures below 30°K where the mean free path of thermal phonons is likely to be larger than the ultrasonic wavelength. The absorption of transverse waves follows in magnitude, as well as in the dependence on temperature and frequency, as expected for a three-phonon process. However, the measured absorption per cm for longitudinal waves depends only slightly on frequency in contrast to the expectations for a four-phonon process; instead it supports a different absorption mechanism discussed here in detail. Finally, experiments with imperfect and neutron-irradiated quartz are reported in which strong additional absorption appears, which may be related to the absorption in fused quartz.