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

In case of open pipe, the frequency of second harmonic is , `f_(1)=2upsilon//2L=upsilon//L`
In case of closed pipe, the frequency of `nth` harmonic is `f_(2)=n upsilon//4L=nf_(1)//4`
where`,n=1,3,5 ..... i.e.n` odd and `f_(1)gtf_(2).`
It will be so if `n=5.`
`:. f_(2)=(5)/(4)f_(1)`