If the frequency of first harmonic of a closed pipe is in unison with the third harmonic of an open pipe. Then, the ratio of lengths of the pipe closed at one end to the open at both the ends is

Options

A. `(1)/(12)`
B. `(3)/(4)`
C. `(1)/(6)`
D. `(6)/(7)`

Answer

C

Explanation

Let `L_(c)` and `L_(o)` be the lenghts of the closed and the open pipes respectivley.
For closed pipe. The frequency of first harmonic `n_(c) = (v)/(4L_(c))`
For open pipe
The frequecy of third harmonic
`n_(0) = (3v)/(2L_(0))`
As `n_(c)` is in unison with `n_(0)`
`therefore " "n_(c) = n_(0)`
`(v)/(4L_(c)) = (3v)/(2L_(0))`
`rArr (L_(c))/(L_(0)) = (1)/(6)`