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As an engineer I see it like this. Imagine I send a wave and then I send another wave in phase shift to cancel that wave. Unless I am sending the wave from exactly the same point in both instances, then I will not have perfect destructuve interference everywhere. Now if I do send the wave and the phase shifted wave from the same location, then it is as if I try to push a cart and pull a cart at the same time. The forces will cancel out and there is no net energy or force. The point I am trying to make is that in practice there will be a small separation between the origin of my two waves and hence there will be areas of destructive and of constructive interference as I cannot perfectly overlap the waves. Does this make sense to you Physicists?

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  • $\begingroup$ Related: physics.stackexchange.com/q/434024/165813 $\endgroup$ – Gilbert Oct 21 '18 at 2:46
  • $\begingroup$ You are correct. Some people don’t seem to understand that. $\endgroup$ – Dale Oct 21 '18 at 2:53
  • $\begingroup$ What if you create the second wave half a wavelenght from the origin of the first other wave, with the right phase? $\endgroup$ – Wolphram jonny Oct 21 '18 at 3:05
  • $\begingroup$ On a transmission line there are no two directions with small separation. The way energy is conserved is not by troughs and crests but by not having any waves at all, for all energy is reflected back to the source if the waves have the correct amplitudes and phases. $\endgroup$ – hyportnex Oct 21 '18 at 13:58
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You are right about what happens in reality. But physical models are simple, and generally, they don't care about practical nuances like this.

So, according to any physical model, even when you emit two waves like that (from the same point, with precisely the phase difference that you want), the mathematical background implies that the model should hold.

Thus it doesn't matter what happens in reality, from the point of view of the theoretical framework. In fact, these kinds of thought experiments can even be used to test the validity of the model, because the model's predictions shouldn't cause any contradictions to the assumptions on which it is based.

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