Question

The fundamental frequency of an air column in a pipe closed at one end is in unison with the third overtone of an open pipe. Calculate the ratio of the lengths of their air columns.

Answer 1

Pipe closed at one end : fundamental frequency,

n_c = \(\frac v{4L_c}\)

column is 51.8 cm.

n_o = \(\frac v{2L_o}\)

In this case, the frequency of the third over tone = \(\frac {4v}{2L_o}\) = \(\frac {2v}{L_o}\)

By the data, \(\frac v{4L_c}\) = \(\frac {2v}{L_o}\)

∴ \(\frac {L_o}{L_c}\) = 8 or \(\frac {L_c}{L_o}\) = \(\frac18\)