Cancellation (destructive interference) occurs at superposition of a crest and a (n):

crest

trough

node

barrier

A noise-cancellation speaker emits a sound wave with the same amplitude but with inverted phase (also known as antiphase) to the original sound. The waves combine to form a new wave, in a process called interference, and effectively cancel each other out - an effect which is called destructive interference.

trough