An organ pipe P 1 closed at one end has vibrating air column in its first overtone and another pipe P 2 open at both ends has vibrating air column in the third overtone, which are in resonance wit

Question

An organ pipe P 1 ​ closed at one end has vibrating air column in its first overtone and another pipe P 2 ​ open at both ends has vibrating air column in the third overtone, which are in resonance with a given tuning fork. The ratio of the length of pipe P 1 ​ to that of P 2 ​ is

TestHub · Accepted Answer

Since, both pipes are in resonance with a given tuning fork, therefore, they will have the same frequency of vibration. For the organ pipe closed at one end. First overtone $(n = 3)$ , .
For organ pipe open at both ends, Third overtone $(n = 4)$ ,
From (1) and (2) $\frac{3 v}{4 l _{1}} = \frac{4 v}{2 l _{2}} \Rightarrow \frac{l _{1}}{l _{2}} = \frac{3}{8}$

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