In the present work, the acoustic waves in X-cut quartz crystals subjected to uniaxial stress were used as a tool for investigation the ferrobielastic twinning phenomenon. The propagation characteristics of media was measured using the previously developed composite resonator spectroscopy. Al-ZnO-Al layers were deposited on one of the X-faces of quartz samples forming composite resonators structures. It was observed that the position of peaks for longitudinal waves increased with the increase of the compressive stress. The ferrobielastic switching was characterized by an abrupt decrease of frequency of peaks. Subsequent increase of pressure resulted in the smaller slope of frequency vs. stress dependence than before twinning. The quantitative and qualitative explanation of the observed data and the evaluation of the sound velocity are given.