Question

The thickness of piezoelectric crystal (PZT5A) used in ultrasound applications will determine the resonant frequency of the transducer. To work at a resonance frequency of 5 MHz, the thickness of a PZT5A transducer must be ________ mm (rounded off to three decimal places).

Hint:

For resonant frequency, the thickness of the piezoelectric crystal is inversely proportional to the frequency.

Answer 1

Correct Answer: 0.434

The resonant frequency \(f\) of a piezoelectric transducer is related to the thickness \(d\) and the velocity of sound \(v\) in the material by the formula: \[ f = \frac{v}{2d} \] Given: \(f = 5\ \text{MHz} = 5 \times 10^6\ \text{Hz}\), \(v = 4350\ \text{m/s}\) Solving for thickness \(d\): \[ d = \frac{v}{2f} = \frac{4350}{2 \times 5 \times 10^6} = \frac{4350}{10^7} = 0.435\ \text{m} \] Convert to millimeters: \[ d = 0.435 \times 1000 = 435\ \text{mm} \] Thus, the required thickness lies between: \[ \boxed{0.434\ \text{to}\ 0.436\ \text{mm}} \] Final Answer: 0.434–0.436 mm