A quartz crystal

For a primary vibration, we have

$\displaystyle f_1 = \frac{c}{2l} \hspace{6cm} \displaystyle \small \text{where} \ c = \sqrt{ \frac{E}{s}}$ ,

For a quartz crystal, $s= 2.65 \ \text{gcm}^{-3}, E= 8 \cdot 10^{11} \ \text{dyn} \ \text{cm}^{-2}$ , so the speed is

$\displaystyle c= \sqrt{ \frac{8 \cdot 10^{11}}{2.65}} \ \text{cm} \ \text{s}^{-1} = \sqrt{ \frac{80}{2.65}} 10^5 \ \text{cm} \ \text{s}^{-1} = 5.5 \cdot 10^5 \ \text{cm} \ \text{s}^{-1} = 5.5 \ \text{km} \ \text{s}^{-1}$

So the frequence of the primary vibration is

$\displaystyle f_1= \frac{5.5 \cdot 10^5}{2} = \boxed{275000 \ \text{Hz}}$