An open and closed organ pipe have the same length the ratio pth mode of frequency of vibration of air in two pipe is

Options

A. p(2p+1)
B. 2p/2p-1
C. p
D. 1

Answer

B

Explanation

For open , fundamental frequency of `P^(th)` mode of vibration is
`n_1 = P(V)/(2l)" " …(i)`
For closed pipe , fundamental frequency of `P^(th)` mode of vibration is
`n_2 = (2P-1)(V)/(4l) " "….(ii)`
From eqn (i) and (ii),
`n_1/n_2 = Pxx((V)/(2l))/((2P - 1) (V)/(4l)) = (2P)/(2P-1)`