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

D

Explanation

First harmonic of a closed organ pipe
`L_(c)=(3 lambda)/(4)`
third harmonic of an open organ pipe
`L_(0)=(3lambda)/(2)`
`(L_( C))/(L_(o))=(3pi)/(4)xx(2)/(3lambda)`
`=(2)/(4)=(1)/(2)`
`:. (L_(C))/(L_(O))=(1)/(2)`