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  4. A closed pipe and an open pipe have their first overtones identical in frequency. Their lengths are in the ratio

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Q. A closed pipe and an open pipe have their first overtones identical in frequency. Their lengths are in the ratio

NTA AbhyasNTA Abhyas 2020Waves

Solution:

If it is given that First overtone of closed pipe = First overtone of open pipe
$\Rightarrow 3 \left(\right. \frac{\nu}{4 l_{1}} \left.\right) = 2 \left(\right. \frac{\nu}{2 l_{2}} \left.\right) ; where \, \, l_{1} and \, \, l_{2}$
are the lengths of closed and open organ pipes hence $\frac{\textit{l}_{1}}{\textit{l}_{2}} = \frac{3}{4}$