Question

Find the ratio of length of a closed pipe to that of the open pipe in order that the second overtone of the former is in unison with fourth overtone of the latter.

Answer 1

Let v and v’ be the fundamental frequencies of the open and the closed pipes respectively of lengths L and L’.

where v is the speed of sound

Second overtone of the closed pipe = 5v’

Fourth overtone of the open pipe = 5v

Since the two notes are to be in unison,

5v’ = 5v or v’ = v

Thus, from eqns. (i) and (ii)