longitudinal wave and transverse wave 
A medium means a thing conveying a wave. For example, air and liquid and metal. A circle of radius r centered at the origin in the xy plane. Object starting point at time t = 0 (r, 0), and movement at an angular velocity ω (rotation angle per unit time). Movement called "single vibration" is the reciprocating motion of the shadow (orthogonal projection) that can be wall shed light parallel to the object to be uniform circular motion. Waves this movement is basic. Simple oscillation animation(HTML5) White：radius Green：second Blue ：orthographic projection
Transverse wave
You pay attention to only the left particle first.
You see that motion of it is a simple oscillation.
Then you watch the second of the left.
You se the prticle is delayed a little than the left particle and does the same movement.
Each particle is delayed a little than the next particle and moves up and down. That makes the vertical wave travels through the air.
We realize that a wave comes to the right from the left, watching the whole of this movement.
Longitudinal wave
The particle of the medium advances to the progress method of the wave. At that time, the wave is the vertical wave.
A particle conveys a wave in the next one then, and going to come back to the original position.
A compression is a point on a medium through which a longitudinal wave is traveling that has the maximum density.
A rarefaction is a point on a cedium through which a longitudinal wave is traveling that has the minimum densiity.
Convert longitudinal wave to transverse wave
For a longitudinal wave, it is not so easy to see on a graph. For a transverse wave we see that the graph looks very similar to the actual wave. 【Procedure】- If a particle moves from a base to the right, it moves up.
- If a particle moves from a base to the left, it moves down.
