Question

In mechanical wave, what do the terms crests and troughs mean?

Answer 1

A crest is the point on a wave with the maximum value or upward displacement within a cycle. A trough is the opposite of a crest, so the minimum or lowest point in a cycle

Answer 2

or u can use wikipedia
http://en.wikipedia.org/wiki/Crest_(physics)

Answer 3

Crest and trough are just name of part of a wave . The highest value a wave is taking is known as crest and the minimum value the wave is taking is known as Trough - this all in a cycle.

The displacement between 'consecutive' trough and trough OR 'consecutive' crest and crest is known as A Cycle.