The frequency of the second overtone of the open pipe is equal to the frequency of first overtone of the closed pipe. The ratio of the lengths of the open pipe and the closed pipe is

Options

A. `2 : 1`
B. `1 :2`
C. `1:3`
D. `3:1`

Answer

A

Explanation

Frequency of the second overtone (ie. Third harmonic) of the open pipe is
`v= (3V)/(2L_(O))` …(i)
where v is the speed of sound in air and `L_(O)` is the length of the open pipe.
Frequency of the first overtone (i.e. third harmonics of the closed pipe is
`v' = (3v)/(4L_(C))` ..(ii)
As per question, v= v'
`:. (3v)/(2L_(O)) = (3v)/(4L_(C)) or (L_(O))/(L_(C)) = (2)/(1)`