Tunnel can be regarded as a column with open ends. For pressure waves the ends of the tunnel, as they are open to atmosphere, at resonance will be nodes of standing waves. This requirement fixes wavelengths, , of standing waves at resonance in terms of the length of the tunnel, L, which we are considering an as open-ended resonance column. We have

We next calculate the wavelengths corresponding to frequencies

For,

For

We have to find integers and which will satisfy that

As we are considering two successive overtones we may use that

This implies that

From this result we can obtain the length of the tunnel. It is given by the relation that