An open and a closed organ pipe are of same length. The ratio of the frequency of the $n^{th}$ mode of vibration of the two pipes is
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For an open pipe in nth mode of vibration,
$\left(v_{n}\right)_{0}=\frac{n v}{2 l}$
For a closed pipe, $\left(v_{n}\right)_{c}=(2 n-1) \frac{v}{4 l}$
$\frac{\left(v_{n}\right)_{0}}{\left(v_{n}\right)_{c}}=\frac{n\left(\frac{v}{2 l}\right)}{(2 n-1) \frac{v}{4 l}}=\frac{2 n}{2 n-1}$
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