$\left(\ell_1 \Rightarrow \text { initial length of pipe }\right)$

$\left(\frac{ V }{ V - V _{ T }}\right) f =\frac{ k }{\ell_2}\left\{ V _{ T }\right.$ Speed of tuning fork, $\ell_2 \rightarrow$ new length of pipe $\}$

$\text { (1) } \div(2)$

$\frac{ V - V _{ T }}{ V }=\frac{\ell_2}{\ell_1}$

$\frac{\ell_2}{\ell_1}-1=\frac{ V - V _{ T }}{ V }-1$

$\frac{\ell_2-\ell_1}{\ell_1}=\frac{- V _{ T }}{ V }$

$\frac{\ell_2-\ell_1}{\ell_1} \times 100=\frac{-2}{320} \times 100=-0.625$

Therefore smallest value of percentage change required in the length of pipe is $0.625$