Two vibrating strings of the same material but lengths \( L \) and ...

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Two vibrating strings of the same material but lengths \( L \) and \( 2 L \) have radii \( 2 r \) and \( r \) respectively. They are stretched
\( \mathrm{P} \) under the same tension. Both the strings vibrate in their fundamental modes, the one of length \( L \) with frequency \( n_{1} \)
W and the other with frequency \( n_{2} \). The ratio \( n_{1} / n_{2} \) is given by
[IIT-JEE (Screening) 2000]
(a) 2
(b) 4
(c) 8
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