An organ pipe `P_1` closed at one end vibrating in its first overtone and another pipi `P_2`, open at both ends vibrating in its third overtone are in resonance with a given tuining fork. Then, the ration of lengths of `P_1` and `P_2` respectively are given by

Options

A. `1:1`
B. `1:3`
C. `3:8`
D. `3:4`

Answer

C

Explanation

Frequency of first overtone of `P_1` pipe `n_1=(3v)/(4l_1)`
Frequency of first overtone of `P_2` pipe `n_2=(4v)/(2l_2)` At resonance `n_1=n_2`
`implies (3v)/(4l_1)=(4v)/(2l_2)`
`l_1/l_2=(3xx2)/(4xx4)`
`l_1:l_2=3:8`