Thermal microwave phonons have been generated in thin resistive films deposited on X-cut quartz and sapphire crystals. The propagation characteristics of these teracycle phonons have been measured in these crystals, and the data have been analyzed using computer techniques. For this work, thin-film, superconducting bolometers were used as the phonon pulse-detecting element with apparently high sensitivity. The results indicated the onset of elastic dispersion in quartz.