• # question_answer Young's modulus for quartz is A) $7\times {{10}^{11}}\,N/{{m}^{2}}$     B) $8.76\times {{10}^{12}}\,N/{{m}^{2}}$ C)  $2\times {{10}^{12}}N/{{m}^{2}}$      D)  Information insufficient

For fundamental tone, $\frac{\lambda }{2}=s\,\,\Rightarrow \,\,\,\lambda =2s$ Here, s is the thickness of the plate Velocity of wave is $v=\sqrt{\frac{Y}{\rho }}$, where Y is Young's modulus of quartz and p is its density. From    ${{f}_{0}}=\frac{v}{\lambda }=\frac{2.87\times {{10}^{4}}}{s}$ or         $\sqrt{\frac{Y}{\rho }}\times \frac{1}{2s}=\frac{2.87\times {{10}^{4}}}{s}$ $\Rightarrow$            $Y=8.76\times {{10}^{12}}\,N/{{m}^{2}}$