A trough is a point on a wave with the maximum value of downward displacement within a wave-cycle. A crest is the opposite of a trough, so the maximum or highest point in a wave-cycle.
- On a wave at sea, the trough is the lowest point in the wave cycle, where the water displacement is furthest down from its rest position. A crest, on the other hand, is the highest point where the displacement is furthest up.
- For electromagnetic waves, which have electric and magnetic fields, a trough on either axis represents the point where the field reaches its minimum value in the downward direction. A crest represents the point of maximum value in the upward direction.