Why is it that when a transverse wave is reflected from a 'rigid' surface, it undergoes a phase change of $\pi$ radians, whereas when a longitudinal wave is reflected from a rigid surface, it does not show any change of phase? For example, if a wave pulse in the form of a crest is sent down a stretched string whose other end is attached to a wall, it gets reflected as a trough. But if a wave pulse is sent down an air column closed at one end, a compression returns as a compression and a rarefaction returns as a rarefaction.
Update: I have an explanation (provided by Pygmalion) for what happens at the molecular level during reflection of a sound wave from a rigid boundary. The particles at the boundary are unable to vibrate. Thus a reflected wave is generated which interferes with the oncoming wave to produce zero displacement at the rigid boundary. I think this is true for transverse waves as well. Thus in both cases, there is a phase change of $\pi$ in the displacement of the particle reflected at the boundary. But I still don’t understand why there is no change of phase in the pressure variation. Can anyone explain this properly?
Best Answer
Great question!
You might have learned that the amplitude of compression and the amplitude of particle displacements are not synonymous. In fact, the maximum amplitude of pressure and the maximum amplitude of particle displacements are out of phase for $\pi/2$. And twice $\pi/2$ (one for original, and one for the reflected wave) accounts for the missing $\pi$ in the phase change of particle displacement.
Imagine, that rarefaction travels towards the wall, which is on the right side. On the moment the wave strikes the wall, maximum displacement is left of rarefaction, that is $\pi/2$ behind it. The same is true for the reflected wave, that is, maximum displacement is again left of the rarefaction, only the direction of the wave is opposite, so maximum displacement amplitude is $\pi/2$ in front of rarefaction.
Thus, the phase of particle displacement changes phase for $\pi$, while the phase of pressure does not change at all at rigid surface.