Physics - Sound Wave Question with Solution | TestHub

The wave speed in string is given by $v_w=\sqrt{\frac{T}{\mu }}$, where, $T$ is tension and $\mu =\frac{m}{l}$ is linear mass density.

Putting the values, we have

$\Rightarrow 60=\sqrt{\frac{T}{10\times {10}^{-3}}\times 0.5}$

$\Rightarrow T=\frac{{\left(60\right)}^2\times {10}^{-2}}{0.5}=72 \mathrm{N}$

The Young's modulus is given by $Y=\frac{Fl}{A∆l}$, here, $A$ is area.

From above the extension of the wire is $\Delta l=\frac{Tl}{AY}=\frac{72\times 0.5}{2\times {10}^{-6}\times 1.2\times {10}^{11}}$$=\frac{72\times 5}{24}\times {10}^{-5}=15\times {10}^{-5} \mathrm{m}$.

Hence, the value of $x=15$.