Constructive Interference:
A constructive interference is when two crests from different sources collide, causing their energies to combine and displace the medium. It creates a crest that is equal to the sum of the two crests where they collide, and then the crests separate and continue on the way they were before the combined.
Destructive Interference:
A destructive interference is when a crest and a trough interfere with each other, causing their energies to combine and work against one another. This makes the waves cancel each other out.
Standing Wave:
The standing wave in this video has 3 nodes (points that remain at rest throughout the interference of pulses). Standing waves are caused when waves with the same amplitude and wavelength interfere with each other. This results in a pattern that remains nearly stationary.
How do noise cancelling headphones work?
The headphones have a microphone placed inside that listens to external sounds that cannot be blocked passively. The electronics inside then use this noise input from the microphone and generate a wave with the same frequency and amplitude as the incoming waves. They then send out a 180 degree copy of this wave made from the noise which cancels each other out as a destructive interference.