The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20\, cm,$ the length of the open organ pipe is .... $cm$
NEET 2018, Medium
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For closed organ pipe, third harmonic is $\frac{3 v}{4 l}$
For open organ pipe, fundamental frequency is $\frac{v}{2 l^{\prime}}$
Given, third harmonic for closed organ pipe
$=$ fundamental frequency for open organ pipe.
$\therefore \quad \frac{3 v}{4 l}=\frac{v}{2 l^{\prime}} \Rightarrow l^{\prime}=\frac{4 l}{3 \times 2}=\frac{2 l}{3}$
where $l$ and $l^{\prime}$ are the lengths of closed and open organ pipes respectively.
$l^{\prime}=\frac{2 \times 20}{3}=13.33 \mathrm{cm}$
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