An organ pipe A closed at one ends is allowed to vibrate in its first harmonic and another pipe B open at both ends is allowed to vibrate in its third harmonic. Both A and B are in resonance with a given tuning fork. The ratio of the length of A and B is

Options

A. `(8)/(3)`
B. `(3)/(8)`
C. `(1)/(6)`
D. `(1)/(3)`

Answer

C

Explanation

`(1)/(6)`
Frequency of closed organ pipe (at one end) `f_(1) = (v)/(4 l_(1))`
Frequency of open organ pipe 3rd harmonic `f_(2) = (3v)/(2l_(2))`
If , `f_(1) = f_(2) implies (v)/(4l_(1)) = (3v)/(2l_(2))`
Ratio of length A and B , `(l_(1))/(l_(2)) = (2)/(12) = (1)/(6)`