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
Correct Answer: B
Solution :
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 \[\sqrt{\frac{Y}{\rho }}\times \frac{1}{2s}=\frac{2.87\times {{10}^{4}}}{s}\] \[\Rightarrow \] \[Y=8.76\times {{10}^{12}}\,N/{{m}^{2}}\]
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