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  4. If a closed organ pipe has the same third harmonic frequency as that of an open organ pipe, then their respective lengths are in the ratio

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Q. If a closed organ pipe has the same third harmonic frequency as that of an open organ pipe, then their respective lengths are in the ratio

KEAMKEAM 2015

Solution:

Third harmonic
$
\begin{array}{l}
\Rightarrow \frac{3 v }{4 l _{e}}=\frac{3 v }{2 l _{ o }} \\
\Rightarrow \frac{ I _{ c }}{ l _{ o }}=\frac{2}{4}=\frac{1}{2}
\end{array}
$
Hence, we get
$
=1: 2
$