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

The frequency of note produced in the pth mode of
vibration in closed organ pipe is
`v_(open)=(pv)/(2l) `
The frequency of note produced in the pth mode of
vibration in closed organ pipe is
`v_(closed)=((2p-1)v)/(4l) `
`therefore` Ratio of pth mode of frequency of vibration of air in two
pipes is
`(v_(open))/(v_(closed)) = (pv//2l)/((2p-1)v//4l)=(2p)/(2p-1)`