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. `3/5`
B. `8/3`
C. `1/6`
D. `1/8`

Answer

C

Explanation

First harmonic of a pipe closed at one end `(n_(c))`
= Third harmonic of a pipe open at both ends `(3n_(o))`
`:. v/(4L_(c)) = 3 (v/(2L_(o)))`
` 12L_(c) = 2L_(o)`
` :. L_(c)/L_(o) = 1/6`