A wave is disturbance which propagates energy from one place to other without transport of matter.
A familiar example is the ripples formed on the surface of water when a stone is thrown on water in a pond. The ripple travels in concentric circles of ever increasing radius till they strike the boundary of the pond.

Types of waves:
Longitudinal wave: If the vibrations of the particles of the medium conveying a wave are to and fro and parallel to the direction of propagation of the wave, then the wave is called a longitudinal wave.

Transverse wave: If the vibrations of the particles of the medium conveying a wave are perpendicular to the direction of propagation of the wave, the wave is called a transverse wave.
Longitudinal wave vs Transverse wave

Longitudinal waveLongitudinal wave
Transverse wavesTransverse wave
Particles in the medium vibrate parallel to the direction of propagation of the wave.
The particles of the medium vibrate perpendicular to the direction propagation of the wave.
The wave travels in the form of condensations and rarefactions.
The wave travels in the form of crests and troughs.
One condensation and a rarefaction constitute one wave.
One crest and one trough constitute one wave.
This cannot be polarized.
This wave can be polarized.

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