A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. What is the ratio of lengths
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(a) Let ${l_1}$ and ${l_2}$ be the length’s of closed and open pipes respectively. (Neglecting end correction)
${l_1} = \frac{{{\lambda _1}}}{4} \Rightarrow {\lambda _1} = 4{l_1}$ and ${l_2} = \frac{{{\lambda _2}}}{2} \Rightarrow {\lambda _2} = 2{l_2}$
Given ${n_1} = {n_2}$ so $\frac{v}{{{\lambda _1}}} = \frac{v}{{{\lambda _2}}} $
$\Rightarrow \frac{v}{{4{l_1}}} = \frac{v}{{2{l_2}}} = \frac{{{l_1}}}{{{l_2}}} = \frac{1}{2}$
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