That is not a very good explanation. This is better, I think: If the initial wave is an impulse of finite duration and finite attack and decay then there will be a spectrum consisting of an infinite number of frequencies which rolls off at 1/ttransitions. The filtering (dispersion) effect of the propagation on the conical wave will suppress the high frequencies and only the very low frequencies will survive as far as the ground.The notion of phase gives me a problem because it implies some natural frequencies of oscillations. Isn't the shock wave more random than that? There must be turbulence but are the modes well defined if it's possible to have a spectrum of wavelengths which can interfere in some way. Trouble is that the verbal handwaving that I have read in the popular discussions doesn't do any more than say 'this or that' happens.
It would be interesting to know if there is an audio recording of the shock wave in the close vicinity of the plane.
Supersonic shock waves are frequent with high velocity rifles but the initial explosion could interfere with hearing just the shock wave