Q 11-14-061JEE MainJEE Main 2023 (12 Apr, Shift 1)Easy
For a certain organ pipe, the first three resonance frequencies are in the ratio of $1:3:5$ respectively. If the frequency of fifth harmonic is $405\ \text{Hz}$ and the speed of sound in air is $324\ \text{m s}^{-1}$, the length of the organ pipe is ______ m.
Numerical value type. Enter your answer.
Answer: 1
Odd harmonics only means a closed pipe. $5f_0=405\Rightarrow f_0=81\ \text{Hz}=\dfrac{v}{4L}\Rightarrow L=\dfrac{324}{324}=1\ \text{m}$.
Solution by Sreeraj P, M.Sc Physics