The speed of a transverse wave passing through a string of length...

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

Putting the values, we have

$⇒ 60 = \sqrt{\dfrac{T}{10 \times {10}^{- 3}} \times 0 . 5}$

$⇒ T = \dfrac{{\left(60\right)}^{2} \times {10}^{- 2}}{0 . 5} = 72N$

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

From above the extension of the wire is $\Deltal = \dfrac{Tl}{AY} = \dfrac{72 \times 0 . 5}{2 \times {10}^{- 6} \times 1 . 2 \times {10}^{11}}$$= \dfrac{72 \times 5}{24} \times {10}^{- 5} = 15 \times {10}^{- 5}m$.

Hence, the value of $x = 15$.