An open pipe is in resonance in `2nd` harmonic with frequency `f_(1)`. Now one end of the tube is closed and frequency is increased to `f_(2)` such that the resonance again ocuurs in `nth` harmonic. Choose the correct option

Options

A. `n =3,f_(2) = (3)/(4) f_(1)`
B. `n =3,f_(2) = (5)/(4) f_(1)`
C. `n=5,f_(2) = (5)/(4) f_(1)`
D. `n =5,f_(2) = (3)/(4) f_(1)`

Answer

C

Explanation

`f_(1)=(v)/(l)` (2nd harmonic of open pipe)
`f_(2)=n((v)/(4l))(n^(th)` harmonic of closed pipe)
Here, n is odd and `f_(2) gt f_(1)`
It is possible when n = 5 because with n = 5
`rArr f_(2)=(5)/(4)((v)/(l))=(5)/(4)f_(1)`