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

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

(a) 8/3

(b) 3/8

(c) 1/2

(d) 1/3

Ans: (b)

Sol:  Frequency of first overtone for closed organ pipe P1 is

$\displaystyle \nu_1 = (2\times 1 + 1)\frac{v}{4l_1}$

$\displaystyle \nu_1 = \frac{3 v}{4l_1}$

Frequency of third overtone for open organ pipe P2 is

$\displaystyle \nu_2 = \frac{4 v}{2l_2}$

According to question ,

ν1 = ν2

$\displaystyle \frac{3 v}{4l_1} = \frac{4 v}{2l_2}$

16 l1 = 6 l2

$\displaystyle \frac{l_1}{l_2} = \frac{3}{8}$