Question

A piezoelectric quartz crystal of thickness 0.005 m is vibrating in resonance conditions. Calculate the fundamental frequency $f_0$ for quartz. ($\gamma =8\times {10}^{10}N{m}^{-2}and\rho =2.65\times {10}^{3}kg{m}^{-3}$)

• A. 5.5 MHz
• B. 55 MHz
• C. 0.55 MHz
• D. 5.5 kHz

Answer 1

Answer: (C)

0.55 MHz

$v=\sqrt{\frac{\gamma }{\rho }}=\sqrt{\frac{8\times {10}^{10}}{2.69\times {10}^3}}$
$=5.5\times {10}^{3}m{s}^{-1};$
$f=\frac{v}{\lambda }=\frac{5.5\times {10}^3}{2\times 0.005}=5.5\times {10}^{5}Hz.$