2023 Manipur WavesHarmonics in closed and open organ pipes Medium Question 6 of 59 in Waves

The 4th overtone of a closed organ pipe is same as that of 3rd overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:

A 8 : 9
B 9 : 7
C 9 : 8
D 7 : 9

The answer is C.

Solution

For a closed pipe, $n_{cop}=(2M+1)^{th}$ harmonic $=(2\times4+1)\times\dfrac{V}{4\ell_c}=\dfrac{9V}{4\ell_c}$ (4th overtone). For an open pipe, $n_{oop}=(M+1)^{th}$ harmonic $=(3+1)\dfrac{V}{2\ell_o}=\dfrac{4V}{2\ell_o}$ (3rd overtone). Equating: $\dfrac{9V}{4\ell_c}=\dfrac{4V}{2\ell_o}\Rightarrow\dfrac{\ell_c}{\ell_o}=\dfrac{18}{16}=\dfrac{9}{8}$.

Concept Harmonics in closed and open organ pipes

Waves in past papers

59 questions from this chapter have appeared across 25 exam years.