The crystal thickness and transducer frequency are related. The thinner the crystal:

• A. The lower the frequency
• B. There is no appreciable effect
• C. None of the above
• D. The higher the frequency

Answer: (D)

In thickness-mode ultrasonic transducers, the crystal thickness sets the resonant frequency because the crystal acts like a small resonator where a half-wavelength fits across the thickness. The resonant frequency follows f ≈ v/2t, with v being the acoustic velocity in the crystal. So, as the thickness t decreases, the resonant frequency increases. This is why thinner crystals produce higher center frequencies.

For a rough intuition, if the velocity is about 4,000 m/s, a 1 mm thick element resonates around 2 MHz, and halving the thickness to 0.5 mm raises the resonance toward 4 MHz. Practically, higher frequency gives better axial resolution but less penetration, while lower frequency (thicker crystal) penetrates more but with coarser resolution.

Therefore, thinner crystals lead to higher frequencies, matching the given correct choice.