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

Options

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

Answer

C

Explanation

`f_(1)=f_(2),(v)/(lamda_(1))=(v)/(lamda_(2))rArr lamda_(1)=4L_(1)=lamda_(2)=(2)/(3)L_(2)`
`rArr (L_(1))/(L_(2))=(2)/(3xx4)=(1)/(6)`