Question

A piezo electric quartz crystal of thickness $0.005\text{m}$ is vibrating in resonate conditions. Calculate the fundamental frequency $f_0$ for quartz.
$Y=8\times {10}^{10}{\text{Nm}}^{-2}$ and $\rho =2.65\times {10}^3{\text{kgm}}^{-3}$

• A. $5.5\text{MHz}$
• B. $55\text{MHz}$
• C. $0.55\text{MHz}$
• D. $5.5\text{kHz}$

Answer 1

The correct option is C $0.55\text{MHz}$

$v=\sqrt{\frac{Y}{\rho }}=\sqrt{\frac{8\times {10}^{10}}{2.65\times {10}^3}}$
$=5.5\times {10}^3{\text{ms}}^{-1}$
$f=\frac{v}{\lambda }=\frac{5.5\times {10}^3}{2\times 0.005}=5.5\times {10}^5\text{Hz}$