Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency $n_1$ and the other with frequency $n_2$. The ratio $n_1/n_2$ is given by
IIT 2000, Medium
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(d) Fundamental frequency $n = \frac{1}{{2l}}\sqrt {\frac{T}{{\pi {r^2}\rho }}} $
where $m =$ Mass per unit length of wire
==>$n \propto = \frac{1}{{lr}} \Rightarrow \frac{{{n_1}}}{{{n_2}}} = \frac{{{r_2}}}{{{r_1}}} \times \frac{{{l_2}}}{{{l_1}}} = \frac{r}{{2r}} \times \frac{{2L}}{L} = \frac{1}{1}$
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