Constructive Interference – happens when two waves (either upper or lower) on the same side collide toward each other, and for a moment combine their energy together, usually resulting in higher amplitude or wavelength.
This shows a constructive interference with both waves being on the top side of the medium (slinky), one crest wave to another. For a second, the energy from both waves would collide and combine, making a taller wave, then they would separate and continue down the medium.
Here is supposed to be the same effect as in the video above, but instead the waves are made facing downward. In this case for demonstration, its shown from side to side.
Destructive Interference – is similar to constructive, but instead the waves that are sent through the medium, one is the top (crest), and one is at the bottom (trough). As they collide together, instead of combining, they cancel each other out for a moment then pass through each other and continue down the medium.
Crest vs Trough
How do noise-cancelling headphones use wave interference to eliminate unwanted sound?
With the idea of wave interference, the headphones have a device inside them that would emit small sound waves. As any noise around in generated, a mic on the headphones measure the frequency and wavelength, then using destructive interference, the device inside the cups would create the same waves that would cancel the outside noise.