We generally describe two types of waves: transverse and longitudinal. A transverse wave is one in which the medium moves from side to side while the wave moves forward. An example of a transverse wave is an ocean swell: the energy may be moving towards shore, but in general the water molecules are moving up and down. For students who have studied trigonomentry, the sine and cosine waves are transverse.

[A transverse wave.]

In contrast, a longitudinal wave is one in which the pulse moves in the same direction as the medium. A good example of a longitudinal wave is a sound wave. Some source of vibration compresses and rarifies molecules of air, and the pulse moves outward to be heard. The molecules wobble back and forth but do not move overall (to prove this to yourself, remember that even though the speed of sound is about 700 miles per hour, you hardly ever cause a hurricane just by speaking!

[A longitudinal, or compression wave.]

All waves can be described with the same mathematical tools. The part of a wave have specific names. The high point is called the crest, and the low point is called the trough. The distance between two consecutive crests (or troughs) is called the wavelength. The difference between the highest and lowest points of a wave are called it's amplitude (and can be increased with an amplifier), and a point in space through which a wave passes without causing action is called a node. Finally, an observer watching waves pass by will be able to count the frequency, how many waves pass in a given length of time.

[A labeled transverse wave]

It is relatively easy to picture the descriptions above with with relation to a tranverse wave, but many students have trouble seeing how they can apply to a longitudinal wave like a sound wave. The key is to remember that all our descriptions of waves will be mathematical. In this case, you could graph the density of a longitudinal wave, and the result is a longitudinal wave.

[A transverse and longitudinal wave. Notice that the transverse wave is a graph of ink used in the longitudinal wave.]

Hazhmirra :D