Wave Phenomena

In this video, we see constructive interference as two crests combined and their energy added into a larger crest

 

In this video, we see an example of destructive interference as a crest and a trough combine and cancel each other out

 

Here we see an example of standing wave where the waves have equal frequency and wavelength and it has two nodes shown.

How do noise-cancelling headphones work?

They use a microphone to measure the ambient noise in the room and then create a negative soundwave of the noise in the room and then integrates it into the sound the listener hears.