Constructed interference:

A constructive interference occurs when a crest from one source meets a crest from another source and their energies combine (additive) to displace the medium.

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Destructive interference :

A destructive interference occurs when a crest and a trough meet, meaning the waves are out of phase and their energies combine to work against each other, resulting in them canceling each other out.

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Standing Wave: 

A standing wave is when interfering waves that have the same amplitude and wavelength, result in an interference pattern that remains nearly stationary at the nodes. Nodes are points that remain at rest throughout the interference of the pulses.

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

Noise cancelling headphones use wave interference to eliminate unwanted sound by producing the necessary sound waves and amplifies them through the headphones, thereby using destructive interference to cancel out the ambient noise.