Constructive interference:

Constructive interference of a wave, is when two waves come together to make a bigger wave. In our video it is tough to see, but at the beginning the wave is much larger and this is where the two waves come together to for a larger one. You can see it goes back down and seems to “split” into two waves, they are actually just continuing onward.

Destructive interference

In our video, It is hard to see, but midway through the video the spring is completely flat and then moves again. Two people pushed the spring in opposite directions with the same force making the spring flat when the two waves meet

Standing waves

A standing wave is where the waves that hit each other are the same in amplitude and their wavelength and what is observed looks almost like it is stuck in place and there are points that never move, the ones closest to the middle.

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

Noise cancelling headphones has microphone which can detect any noise frequencies outside of the earcup and creates very similar sound waves, which cancels out any outside sound. This is called destructive interference.