Why do waves have crests and troughs?
I think your question has come from your observation of waves in a pond or at the seashore. You would get the same impression if you were to shake a string tied to a tree on the other end – you would see a crest travelling to the other end and then, perhaps be reflected back. Like the particles of the rope, the molecules of water in the pond also move up and down; they do not travel in the direction in which the wave travels. The word wave implies that at a given point, some parameter increases and decreases with some periodicity, and this tendency propagates. So crests and troughs are implied but they need not be always normal to the direction of propagation. This is so for water waves, waves in a string and also for light and radio waves. But this is not so for sound waves, for which the crests and troughs are in the density change of the medium through which the wave travels. But let me come back to the exact wording of your question. When you throw a stone in a pond, you depress a