Q: 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 that correct option

(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}

Ans: (c)

Sol: Second harmonic of open pipe , $\large f_1 = 2(\frac{v}{2l}) = \frac{v}{l}$

nth harmonic of closed pipe , $\large f_2 = n(\frac{v}{4l}) $ (here, n is odd)

$\large f_2 > f_1$ (given)

It is possible when n is 5 .

$\large f_2 = 5(\frac{v}{4l}) = \frac{5}{4} f_1$