Question

A piezo - electric quartz plate is vibrating to produce wavelength of ${10}^{-2}m$. Find the frequency, if for quartz, $E=8\times {10}^{10}N{m}^{-2}$ and $\rho =2.65\times {10}^{3}kg{m}^{-3}$

Answer 1

Velocity of sound is given by

$v=\sqrt{\frac{E}{\rho }}$

$frequency\left(f\right)=\frac{velocity\left(v\right)}{wavelength\left(\lambda \right)}$

$\therefore f=\frac{\sqrt{\frac{E}{\rho }}}{\lambda }=\sqrt{\frac{E}{\rho }}\times \lambda =\sqrt{\frac{8\times {10}^{10}}{0.265\times {10}^4}}\times {10}^{-2}$

Please note that whenever there is a square root in a calculation, the powers of 10 should always be converted into even number. For eg:- I have converted $2.65\times {10}^3$ to $0.265\times {10}^4$

By doing this, you can easily take the 10 term outside the root and calculation becomes easier.

$\therefore f=\sqrt{\frac{8\times {10}^6}{0.265}}\times {10}^{-2}=\sqrt{\frac{8}{0.265}}\times {10}^3\times {10}^{-2}=5.5\times 10=55Hz$

The frequency is 55HZ