eli5 How does destructive interference work?

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I understand that it’s basically opposite waves cancelling each other out. But I want to know why it works. Sorry in advance, if I’m not clear.

In: Mathematics

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Assume the top of the wave is +1, and the bottom of the wave is -1. When the waves are opposite the result is +1 + -1 = 0, and likewise -1 + 1 = 0.

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