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Physics

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  • $\begingroup$ You've got zero by the assumption that the waves have exactly the same direction. This is mathematically possible, but in practice, the sources of the two waves are at different places, and the waves will have different directions, and thus their sum won't vanish everywhere. $\endgroup$ Commented Oct 1 at 13:30
  • $\begingroup$ @moshtaba If electric field cancels, the sources do not transmit energy and they do not consume energy. $\endgroup$ Commented Oct 1 at 13:47
  • $\begingroup$ "Assume" we have two sources in $x=0$ and $x=1$ and the later source could passes light of former one through it self completely. Then,,, likely we get nothing... where would go energy transmitted from sources? @JánLalinský $\endgroup$ Commented Oct 1 at 13:49
  • $\begingroup$ The individual EM fields can't be ascribed their respective energies which when summed would give total conserved energy. Instead, EM energy is a property of all the particular fields present (we can express it as sum over all pairs of fields). In your example, the direction of the wave matters, and is different on the left and right of the source. When the wave 2 cancels the wave 1 for $x>1$, it can't cancel it for $0<x<1$. That means we will get, at best, a stationary wave in the interval $(0,1)$. $\endgroup$ Commented Oct 1 at 13:56
  • $\begingroup$ Fields/waves add up to form total wave, which implies how the Poynting energy is distributed. But there are no individual waves energies, which would add up. So there is no problem with energy disappearing where the two waves cancel each other - energy wasn't there at all. $\endgroup$ Commented Oct 1 at 13:58