The frequency of third overtone of a pipe closed at one end , is in unison with the fifth overtone of a pipe open at both the ends. Then the ratio of length of the pipe closed at one end to the open at both the ends is

Explanation

Given that : `n_(3) = n_(0)`.
Where , `n_(3)= ` frequency of the third overtone of the open pipe
`n_(0) = ` fundamental frequency of the blood pipe
Third overtone of open pipe is
`n_(3) = 4((v)/(2L_(3)))`
Fundamental frequency of closed pipe at one end is
`n_(0) = v/(4L_(0))`
Fundamental frequency of closed pipe at one end is
`n_(0 ) = (v)/(4L_(0))`
`v/(4L_(0)) = 4((v)/(2L_(3))) ( :' n_(0) = n_(3))`
`:. (L_(0))/(L_(1)) = 1/8`
`:. L_(0) : L_(3) = 1 : 8`