Defination of wave

A wave is a disturbance which propagates energy and momentum from one place to the other without the transport of matter.

One dimensional wave :

Energy is transferred in a single direction only.
Example : Wave propagating in a stretched string.

Two dimensional wave :

Energy is transferred in a plane in two mutually perpendicular directions.
Example : Wave propagating on the surface of water.

Three dimensional wave :

Energy in transferred in space in all direction.
Example : Light and sound waves propagating in space.

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