A new method for the generation and detection of ultra high-frequency sound waves has been recently described [H. E. Bömmel and K. Dransfeld, Phys. Rev. Letters 1, 234 (1958)]. It is based on piezoelectric surface excitation at the ends of a quartz rod placed between two identical microwave cavities. Longitudinal as well as transverse waves have been generated this way and have been transmitted into other media by means of compressional bond techniques. This method together with the simultaneously discovered fact that the attenuation of hypersonic waves in quartz is very small at temperatures below 15°K should make it now possible to extend ultrasonic research up to frequencies of about 1011 cps. It should allow to investigate problems in solid state and liquid state physics involving phonon-phonon interactions, the interactions of phonons with spins, electrons, rotons, etc., at frequencies approaching those of the thermal phonons at low temperatures. Surface excitation should not be restricted to piezoelectric materials but should also be applicable to magnetostrictive substances as for example in ferromagnetic resonance. The results of hypersonic absorption measurements as a function of temperature in natural, synthetic, and neutron irradiated quartz crystals in the frequency range between 1000 and 4000 mc/sec will be presented.