Reducing resonance in a piezoelectric ultrasonic transducer
Yes, these transducers tend to have high Q, which makes them &quot;ring&quot; like a bell.
In the example below, a 40kHz piezo was measured and fitted to an electronic model that substitutes L-C-R components for the mechanically-resonant components. For this transducer, the electrical equivalents were:

Lm = 92.1 millihenries
Cm = 175.384 picofarads
Rm = 634 ohms

The value of parallel capacitance is real, measured with a capacitance meter: 1.3 nanofarads.


The current through the series arm comprising Lm, Cm, Rm is proportional to physical motion of the transducer. When driven directly from a voltage source, current takes a long time to rise to full amplitude (purple trace, I(R3)).
An external inductor (L2=12.42 mH) along with a damping resistor (R1=5400 ohms) gives a significantly faster, critically damped rise time (green trace). The penalty paid is far less current - making the transducer less sensitive.

The simple approach of damping with a resistor (R1=5400 ohms) is wasteful of available transducer signal. An impedance-matching transformer would be a better, more costly alternative.