An organ pipe `P_(1)` open at one end vibrating in its first harmonicare 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. (a) `8//3`
B. ( b) `3//8`
C. ( c ) `1//6`
D. (d) `1//3`

Answer

C

Explanation

( c )

bhv_(1) = (v)/(4l_(1))` for first harmonic
bh v_(2) = (3v)/(2l_(2))` for third harmonic
`because` `v_(1) = v_(2)` :. `(v)/(4l_(1)) = (3v)/(2l_(2))` rArr `(l_(1))/(l_(2)) = (1)/(6)`