How is a piezoelectric crystal used to generate waves of ultrasound?

A piezoelectric crystal makes use of the peizoelectric effect. This is the production of a voltage when mechanical stress is applied across the material. This occurs only in materials when the unit cells which make up the material have an asymmetric charge distribution when under compression.
The reverse of this is using the crystal to produce waves. This is the reverse peizoelectric effect. This means appying a voltage to the crystal, producing compression. When an alternating current is applied, this gives repeated compression and relaxation of the crystal.
The movement of the face of the crystal will displace air molecules, giving a longitudinal wave, meaning, at the necessary high frequency, ultrasound waves.