The density of the stretched string is changed by 2% without change in tension and radius. The change in transverse wave velocity.

$\mathrm{V}=\sqrt{\frac{\mathrm{T}}{{\mathrm{\pi r}}^2\mathrm{d}}}\mathrm{d}\to$density ; $\mathrm{V}\propto \frac{1}{\sqrt{\mathrm{d}}}$
$\therefore \frac{∆\mathrm{V}}{\mathrm{V}}\%=-\frac{1}{2}\frac{∆\mathrm{d}}{\mathrm{d}}\%$
Change in velocity $\frac{∆\mathrm{V}}{\mathrm{V}}=-\frac{1}{2} \mathrm{x} 2=-1\%$
density decreases $\Rightarrow \frac{∆\mathrm{V}}{\mathrm{V}}>0$
Density increases $\Rightarrow \frac{∆\mathrm{V}}{\mathrm{V}}<0$
$\therefore$The velocity changes by 1% (increases or decrease)