An organ pipe `P_(1)` closed at one end vibrating in its first overtone and another pipe `P_(2)` open at both ends vibrating in third overtone are in resonance with a given tuning fork . The ratio of the length of `P_(1)` to that of `P_(2)` is

Options

A. `1 : 2 `
B. `1 : 3 `
C. `3 : 8 `
D. `3 : 4 `

Answer

C

Explanation

First overtone of closed organ pipe `n_1=(3v)/(4l_1)`
Third overtone of open organ pipe `n_2=(4v)/(2l_2)`
`n_1=n_2` (Given) `rArr (3v)/(4l_1) = (4v)/(2l_2) rArr l_1/l_2 = 3/8`