The thickness of the PZT crystal in a pulsed wave transducer is equal to what fraction of the wavelength?

• A. One-quarter of the wavelength
• B. One-half of the wavelength
• C. Equal to the wavelength
• D. Twice the wavelength

Answer: (B)

In a pulsed-wave transducer the PZT crystal is designed to operate in thickness mode, where the crystal’s thickness is set to about half the acoustic wavelength inside the crystal. This half-wavelength thickness lets a wave traveling through the crystal reflect back and forth to form a standing wave that has maximum motion at the emitting surface, maximizing energy radiated as sound. Since wavelength in the crystal is λ = v/f (v is the speed of sound in the PZT and f is the operating frequency), the thickness that achieves this resonance is t = λ/2. That’s why the thickness is one-half of the wavelength.

If the thickness were a quarter of a wavelength, you’d be off the fundamental resonance and energy transfer would be less efficient; if it were equal to the full wavelength or twice the wavelength, you’d be targeting a different resonance condition or higher-order mode, not the optimal fundamental operation for the intended frequency.