A wave is a disturbance or oscillation that travels through space(dr) and matter with time delay(dt).
The speed of the wave is v=dr/dt. So the delay in time is proportional to the distance traveled. (dr = v *dt).
CLick play at the following simulation.
The blue dot will move up and down, the same disturbance travel to the right.
You can change the dx or dt to see how the wave speed changed
(it means the wave traveled in dfferent media, the wave speed is determined by the media the wave travel through).
You can also drag the blue dot by mouse( up and down), and find out how wave is formed.