The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe 2 m long. The length of the open pipe is

Options

A. ` 8 m `
B. ` 4 m `
C. `2 m`
D. ` 1 m `

Answer

B

Explanation

Let L be the strength of the open pipe. The fundamental frequency of the open pipe is given by `u=(v)/(2L)`, v= velocity of sound in air
The second overtone of the open pipe has a frequency `3v_(O)=(3v)/(2L_(O))Hz`
The length of the closed pipe `L_(C)=2m`.
The fundamental frequency of the closed pipe is given by `v=(v)/(4L)`
The first overtone of the closed pipe has a frequency.
`3v_(c)=(3v)/(4L_(c))=(3v)/(4xx2)=(3v)/(8)Hz`
`"Now", 3v_(0)=3v_(0) or (3v)/(2L_(0))=(3v)/(8)`
`or 2L_(O)=8 or L_(O)=4m`