The frequency of the second overtone of the open pipe is equal to the frequency of first overtone of the closed pipe. The ratio of the lengths of the open pipe and the closed pipe is

Options

A. `2 : 1`
B. `1 : 2 `
C. `1: 3`
D. `3 : 1 `

Answer

A

Explanation

Second overtone of open organ pipe means third harmonic
`therefore` its frequency is `V_(0) = 3.(v)/(2l_(0))`
First overtone of closed organ pipe is `3^(rd)` harmonic so its frequency is `v_(0) = 3 (v)/(4l_(c))`
since `v_(0) = v_(c) `
`therefore " " 3.(v)/(2l_(0)) = 3 (v)/(4l_(c))`
`therefore " " (l_(0))/(l_(c)) = (2)/(l)` So correct choice is (a).