An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P2 open at both ends…

Q: An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P2 open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 and P2 is

(a) 8/3

(b) 3/8

(c) 1/6

(d) 1/3

Ans: (c)

Sol: First harmonic of closed organ pipe = Third harmonic of open organ pipe

$\large \frac{v}{4l_1} = 3 (\frac{v}{2l_2})$

$\large \frac{l_1}{l_2} = \frac{1}{6}$