Describe the physical mechanism by which a piezoelectric transducer detects incoming ultrasound pulses and converts them into an electrical signal.

During an ultrasound scan of an internal organ, such as the liver, a coupling gel is applied to the patient's skin before the transducer is positioned.

Explain, using the concept of acoustic impedance, why this gel is necessary. In your explanation, define acoustic impedance in terms of the physical properties of the medium, state the mathematical formula for the fraction of intensity reflected at a boundary, and compare the transmission at an air-to-skin boundary versus a gel-to-skin boundary.