Which property primarily determines the fundamental frequency of a piezoelectric crystal?

Which property primarily determines the fundamental frequency of a piezoelectric crystal?

• A. The thickness of the crystal
• B. The length of the applied voltage pulse
• C. The amplifying characteristics of the pulse amplifier in the instrument
• D. None of the above

Answer: (A)

The frequency at which a piezoelectric crystal naturally resonates in thickness mode is determined by its thickness. The crystal acts as a standing wave in the thickness direction, and the fundamental resonance occurs when the thickness is about half the acoustic wavelength in the material: t ≈ λ/2. Since λ = v/f, the fundamental frequency is f = v/(2t), where v is the speed of sound in the crystal for that mode. So a thinner crystal resonates at a higher frequency, while a thicker crystal resonates lower, independent of how you drive it. The length of the applied voltage pulse mainly affects the spectral content and bandwidth of what you excite, not the crystal’s inherent resonant frequency. The amplifier’s characteristics influence amplitude and waveform quality but don’t set the fundamental resonance.

The frequency at which a piezoelectric crystal naturally resonates in thickness mode is determined by its thickness. The crystal acts as a standing wave in the thickness direction, and the fundamental resonance occurs when the thickness is about half the acoustic wavelength in the material: t ≈ λ/2. Since λ = v/f, the fundamental frequency is f = v/(2t), where v is the speed of sound in the crystal for that mode. So a thinner crystal resonates at a higher frequency, while a thicker crystal resonates lower, independent of how you drive it.

The length of the applied voltage pulse mainly affects the spectral content and bandwidth of what you excite, not the crystal’s inherent resonant frequency. The amplifier’s characteristics influence amplitude and waveform quality but don’t set the fundamental resonance.