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This video shows two crests colliding with each other. This is called constructive interference. When the two crests collide for he moment, they combine to create one bigger wave

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this video demonstrates destructive interference where a crest collides with a traugh. When they collide they cancel each other out.

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in this last video, we attempted to create a standing wave. In the video you can see the nodes where the destructive interference occurs, and also the crests and traughs where you can see the constructive interference.

How do noise cancelling headphones use wave interference to eliminate unwanted sound?

A microphone inside the ear cup will sense an incoming wave, it will then send and equal negative wave in the other direction towards the incoming wave to eliminate it. The headphones use destructive interference to eliminate incoming sound waves.