Every time I read an article/text about standing waves they seem to specifically mention that whenever a wave pulse hits a hard boundary it gets reflected back with it's phase changed through 180 degrees. My question is why and how does this happen?
Suppose two wave pulses are traveling on a string towards each other. They have the same amplitude except one of the waves are inverted so that when the two superimpose completely the net displacement of the string at that instance becomes zero. Where does the wave energy 'vanish'? And how do the waves continue their motion hence as if nothing out of the ordinary happened?
The change of phase is property of waves. One way to see it, is that the waves are being transmitted and reflected at the same time, so at a hard boundary, we impose the condition that the amplitude must be zero, thus the reflected wave must be out of phase with respect to the incoming (transmitted) wave. Furthermore, there may be places where the local displacement is zero, but when talking about energy conservation you need to take into account the whole string.