Constructive interference: When a crest and a crest or a trough and a trough meet, the energy combines together.
Destructive interference: When a crest and a trough meet, the energy will cancel out.
Standing Waves: When the waves have the same amplitude and wavelength, the pattern will remain and there will be nodal points which are places that remain stationary.
How noise-cancelling headphones use wave interference to eliminate unwanted sound: Noise-cancelling headphones emit the opposite wave of the incoming sound wave making the wave cancel out, and they also absorb the sound. The effect is called destructive interference.