Speed of a transverse wave on a straight wire (mass 6.0g, length 60cm and area of cross-section $1.0m{m}^2$ ) is $90m{s}^{-1}$   . If the Young’s modulus of wire is  $15\times {10}^{11}N{m}^{-2}$  , the extension of wire over its natural length is  $x\times {10}^{-5}$  m. Find the value of $x$  . (Answer the nearest integer)

Speed of transverse wave over a string.
   $v=\sqrt{\frac{T}{\mu }}$ ……(i)
Where T= tension or force on string 
And  $\mu =\frac{m}{l}$  = mass per unit length.
Also, young’s modulus of string 
 $Y=\frac{TI}{A\Delta l}\Rightarrow T=\frac{YA\Delta l}{l}$  ………(ii)
From Eqs.(i) and (ii), we have $v^2=\frac{YA\Delta l}{\mu l}or\Delta I=\frac{m{v}^2}{YA}$   …………….(iii)
Here,  $\text{m = 6g}=6\times {10}^{-3}kg,l=60cm$

$$\begin{gathered} =60\times {10}^{-2}m,A=1m{m}^2 \\ =1\times {10}^{-6}{m}^2, \end{gathered}$$
  $Y=15\times {10}^{11}N{m}^{-2}$ and  $v=90m{s}^{-1}$
Substituting these given values  in Eq. (iii), we get

 $\Delta l=\frac{6\times {10}^{-3}\times {\left(90\right)}^2}{15\times {10}^{11}\times 1\times {10}^{-6}}=3.24\times {10}^{-5}m$