Q 11-14-071JEE MainJEE Main 2022 (25 Jun, Shift 1)Easy
The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is $20\ \text{cm}$, the length of the open organ pipe is ______ cm.
Numerical value type. Enter your answer.
Answer: 80
First overtone of the open pipe: $\dfrac{2v}{2L_o} = \dfrac{v}{L_o}$. Fundamental of the closed pipe: $\dfrac{v}{4L_c}$.
$$\frac{v}{L_o} = \frac{v}{4\times20}\ \Rightarrow\ L_o = 80\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics