Theoretical and experimental studies have been conducted of the transmission of phonons in sapphire and their reflection at a crystal-vacuum interface. The effects of crystal anisotropy on the reflection process are discussed in detail. The heat-pulse technique has been used to obtain high-resolution time-of-flight spectra as a function of the angle of incidence in accurately known crystallographic directions. The agreement with predictions from numerical calculations is excellent. The relevance of these observations to studies of the anomalous transmission of energy through a crystal-liquid helium interface is also discussed
