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

An organ pipe A closed at one ends is allowed to vibrate in its first

1.	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
Answer» `(8)/(3)` `(3)/(8)` `(1)/(6)` `(1)/(3)` SOLUTION :`(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)`