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 occurs in `nth` harmonic. Choose the correct option.

Options

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

Answer

B

Explanation

In case of open pipe, frequency of second harmonics is,
`f_(1)=(v)/(lambda)=(v)/(L) " " [ lambda=L]`
In case of closed, pipe, frequency of `n^(th)` harmonic,
`f_(2)=(mv)/(4L)` where n is odd number.
clearly `f_(2)=(n)/(4)f_(1)`
If `n=3, f_(2) lt f_(1)` which is not acceptable
In `n=5, f_(2)=(5)/(4)f_(1)` which is acceptable