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Q.
An open and a closed pipe have same length. The ratio of frequency of their $n$th overtone is
Waves
Solution:
Let $l$ be the length of the pipes and $v$ the speed of sound Then frequency of open organ pipe of $n$th overtone is
$f_{1}=(n+1) \frac{v}{2 l}$
and frequency of closed organ pipe of $n$th overtone
$f_{2}=(2 n+1) \frac{v}{4 l}$
Therefore, the desired ratio is
$\frac{f_{1}}{f_{2}}=\frac{2(n+1)}{(2 n+1)}$