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Question 32.11: Quartz is an example of a piezo-electric material. The speed...

Quartz is an example of a piezo-electric material. The speed of sound in quartz is 5700  m  s^{−1}.

a Calculate the wavelength of ultrasound waves of frequency 2.1 MHz in a quartz crystal.

b If the crystal is to be used in an ultrasound transducer, its thickness must be half a wavelength. Calculate the thickness of the transducer.

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a Rearrange speed v = fλ to give wavelength
λ = \frac{v}{f} = \frac{5700}{2.1  ×  10^{6}} = 2.7 × 10^{–3}  m (2.7 mm)
b 1.35 × 10^{–3}  m \approx 1.4  mm

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