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  4. A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. The ratio of their lengths is

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Q. A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. The ratio of their lengths is

NTA AbhyasNTA Abhyas 2022

Solution:

Fundamental frequency of close pipe,
$v_{1}=\frac{v}{4 l_{1}}$
Fundamental frequency of open pipe,
$v_{2}=\frac{v}{2 l_{2}}$
But $v_{1}=v_{2}$
$\therefore \frac{l_{1}}{l_{2}}=\frac{1}{2}$