Various types of composite resonators and their uses are summarized. The general equations are given for the transducer for plane ultrasonic waves, consisting of a crystal assembly with back and front plates. Applications are made to several simple cases, and expressions are tabulated for the amplitude of vibration for various combinations of half- and quarter-wave components. Consideration is given to the effect of the acoustic load on the frequency for maximal amplitude. Theoretical formulas are compared with experimental results for rods of aluminum and fused quartz excited in vibration by piezoelectric crystals.