An open pipe is in resonance in 2nd harmonic with frequency f1. Now one end of the tube is closed…

Q: An open pipe is in resonance in 2nd harmonic with frequency f1 . Now one end of the tube is closed and frequency is increased to f2 such that the resonance again occurs in nth harmonic. Choose that correct option

(a) n = 3, f2 = (3/4) f1

(b) n = 3, f2 = (5/4) f1

(c)n = 5, f2 = (5/4)f1

(d) n = 5, f2 = (3/4)f1

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 .

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