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A wave is a mechanism through which energy is transferred from one point to another without transporting matter. It is a disturbance produced in a medium.
There are two types of waves, transverse waves and longitudinal waves.
In a transverse wave, the particles in the wave travel perpendicular to the direction the wave is traveling. Examples are the wave nature of light, and waves on a vibrating string.
In a a longitudinal wave, the particles move parallel to the direction of the wave. Examples are sound, and an expanding and contracting spring.