Constructive: Constructive interference is when a crest from one wave meets a crest from another wave. The energies of the two waves coming towards each other combine to displace the medium. In other words, when a crest meets a crest they combine to make one big crest. When a trough meets a trough, the combine to make one big trough.

Destructive: Destructive interference is when a crest from one wave meets a trough from another wave. The energies of  the two waves combine to work against each other and cancel out the wave.

Standing Waves: A standing wave is when interfering waves have the same amplitude (same distance of the center of the wave to the crest) and wavelength, a pattern occurs where the resultant interference pattern remains stationary. The point which remains at rest is called a node or a nodal point.

How Do Noise Cancelling Headphones Use Wave Interference to Eliminate Unwanted Sound?

Noise cancelling headphones word by using destructive interference. There is a microphone on the earbuds of the headphones that listen to the noise outside the headphones. Then, devices in the headphones sense the noise from the microphone and note things such as frequency and amplitude of the incoming sound waves. Then they create a new wave that is completely out of phase with the waves from the noise. As a result the sound waves from the noise is completely cancelled out.