Microwave phonons at 3.1, 4.7, and 9.3 GHz were generated with CdS thin-film transducers, propagated through Fe 2+-doped MgO at 1.5 K, and detected with a photon-phonon double-quantum detector. In comparing double-quantum detection with the conventional piezoelectric method, it was found that the energy detecting properties of the former yielded exponential decays even when the latter did not. The field, frequency, and angular dependencies of the double-quantum detector were measured and interpreted. A shift from the double-quantum absorption to a slowly decaying saturation signal of opposite sign was observed as the phonon frequency approached that of the photons. The better precision made possible by the exponential echo pattern of the double-quantum detector was used to obtain accurate values for phonon attenuation. The frequency dependence of attenuation in MgO at 1.5°K was measured for the first time. This dependence could be fitted to a term proportional to frequency (of about 0.3dB/cm-GHz) which indicated the presence of scattering from dislocations, and a frequency-independent term (of about 0.4 dB/cm) attributed to boundary scattering. Double-quantum detection was also used to detect the scattered phonons observed between the echoes, and to demonstrate that they represented elastically scattered phonons. Longitudinal to-transverse mode conversion in one sample correlated with the presence of small-angle grain boundaries, as indicated by X-ray diffraction and laser ultramicroscope observations.