Destructive Intereference Question

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When there is destructive interference I know that two waves that are out of phase cancel out, but what really goes on? What i mean is when there is destructive interference are the two waves that are interfereing constantly interfereing or are they both completely eliminated at the initial point of interference and no waves propagate thereafter?
 
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It's at that point the amplitude of the incoming waves continually sum to 0. However, just when two wave interact on a string (see this video ) the wave continue propagate through the interference and afterwards.

That is why you can record the interference at a variety of distances (as long as you are far enough away for your approximations to hold): the waves continually interact destructively and constructively, but the individual waves are unchanged by this process.

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So if two waves that are destructing and are propagating continually and then somehow one of the two waves is shifted using a reflective film, the waves then should no longer destruct, correct?