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

3

Explanation

First overtone of closed pipe `n_(1) =(3v)/(4l_(1))`
Third overtone of open organ pipe `n_(2) =(4v)/(2l_(2))`
`r_(1) = n_(2) ["Given"] rArr (3v)/(4l_(1)) =(4v)/(2l_(2)) rArr (l_(1))/(l_(2)) =(3)/(8)`