This video shows a constructive wave. A constructive wave is when a crest meets another crest coming from the opposite direction. This results in the two crests meeting in the middle to form one big crest.
This video shows a destructive wave. A destructive wave is when a trough meets a crest coming from the opposite direction. This results in the wave hitting each other and bouncing back because they cancel each other out.
This video shows a standing wave. A standing wave is when two waves interact that are the same wavelength and have the same amplitude. The result is a nearly stationary wave.
How do noice-cancelling headphones use wave interference to eliminate unwanted sound? When the electronic device plays music into the headphones waves are produced sending the noise to our ears. The noise cancelling headphones detect the waves and they send out another wave with the same amplitude, which results in a destructive interference and cancelling out unwanted noise.