The Fundamental frequency of a pipe closed at one end is in unison with the second overtone of an open pipe. Calculate the ratio of the length of their air columns. Ignore the end correction.

Explanation

Pipe closed at one end : fundamental frequency `n_(c)= v/(4L_(c))`
Pipe open at both ends : fundamental frequency `n_(0) = v/(2L_(0)) ` In this case, the frequency of the second overtone =` (3v)/(2L_(0))`
By the data = `v/(4L_(c)) = (3v)/(2L_(0) = L_(0)/L_(c) = ( 4xx 3)/2`
` L_(0)/L_(c) = 5 or L_c/L_o = 1/6 ` This is the required ratio.