Q 11-14-043JEE MainJEE Main 2024 (8 Apr, Shift 1)Medium
A closed and an open organ pipe have the same length. If the ratio of frequencies of their seventh overtones is $\left(\dfrac{a-1}{a}\right)$, then the value of $a$ is ______.
Numerical value type. Enter your answer.
Answer: 16
Closed pipe: only odd harmonics; the 7th overtone is the 15th harmonic, $f_c = \dfrac{15v}{4L}$.
Open pipe: all harmonics; the 7th overtone is the 8th harmonic, $f_o = \dfrac{8v}{2L} = \dfrac{16v}{4L}$.
$$\frac{f_c}{f_o} = \frac{15}{16} = \frac{a-1}{a} \;\Rightarrow\; a = 16$$
Solution by Sreeraj P, M.Sc Physics