Explanation

(b) Velocity of sound increases if the temperature increases. So with $v = n\lambda,$ if $v$ increases $n$ will increase
At $27℃,\ v_{1} = n\lambda,$ at $31℃,\ v_{2} = (n + x)\lambda$
Now using $v \propto \sqrt{T}\ \ \ \ \ \left\lbrack \because v = \sqrt{\frac{\gamma RT}{M}} \right\rbrack$
$\frac{v_{2}}{v_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} = \frac{n + x}{n}$
$\Rightarrow \frac{300 + x}{300} = \sqrt{\frac{(273 + 31)}{(273 + 27)}} = \sqrt{\frac{304}{300}} = \sqrt{\frac{300 + 4}{300}}$
$\Rightarrow 1 + \frac{x}{300} = \left( 1 + \frac{4}{300} \right)^{1/2} = \left( 1 + \frac{1}{2} \times \frac{4}{300} \right) \Rightarrow x = 2$
$\lbrack\because(1 + x)^{n} = 1 + nx\rbrack$