If you increase the thickness of the PZT crystal, what happens to the emitted wavelength and frequency?

If you increase the thickness of the PZT crystal, what happens to the emitted wavelength and frequency?

• A. Wavelength increases and frequency decreases
• B. Wavelength decreases and frequency increases
• C. Both increase
• D. Both decrease

Answer: (A)

The key idea is how the crystal’s thickness sets the resonant wavelength and frequency in a piezoelectric transducer. For the fundamental mode, the thickness is tied to about half the wavelength of the sound inside the crystal, so t ≈ λ/2. When you increase thickness, the resonant wavelength grows. Since the wave speed in the crystal stays roughly the same for a given mode, the frequency f = v/λ decreases as λ increases. So thickening the PZT crystal results in a longer emitted wavelength and a lower emitted frequency.

The key idea is how the crystal’s thickness sets the resonant wavelength and frequency in a piezoelectric transducer. For the fundamental mode, the thickness is tied to about half the wavelength of the sound inside the crystal, so t ≈ λ/2. When you increase thickness, the resonant wavelength grows. Since the wave speed in the crystal stays roughly the same for a given mode, the frequency f = v/λ decreases as λ increases. So thickening the PZT crystal results in a longer emitted wavelength and a lower emitted frequency.