Destructive interference happens when a compression and rarefaction section meet and the next effect is that there’s no push or pull on the particles. The waves don’t destroy each other (as the name implies), but rather they cancel out the effect of each other when they interact with each other, which results in no sound at all. Which is kind of odd to think about: two sound waves interacting to make no sound at all. This happens at the nodes, where there’s no particle displacement.
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