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There are two types of wave in terms of mode of vibration of the particles: Longitudinal waves and Transverse waves.
Longitudinal waves:
A wave in which the particles of the medium vibrating in the direction (Parallel) of propagation. Sound wave in air and wave in spring are the example of Longitudinal waves, which are suddenly compressed (Compression) and released (Rarefaction), as shown in figure below. The distance between two nearest Compressions and Rarefaction is equal to one wavelength ($\lambda$).
Fig 1: Longitudinal waves
Transverse waves:
A wave in which the particles of the medium vibrates at right angles (Perpendicular) to the direction of propagation. Waves on water surface, Electromagnetic waves (Light, X-Rays, Micro waves, U-V rays), Vibrating Guitar string are the example of transverse waves.
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| Fig 2: Transverse waves |
During the oscillation, the particle move upward or downward from the plane passing through their mean position. The maximum distance above the mean position is called Crest. And the maximum distance below the mean position is called Trough, as shown in figure below. Thus in the transverse wave Crest and Trough are appear alternatively.
This is the animated video to visualize the Transverse waves and Longitudinal waves[1].
Difference between Transverse and Longitudinal waves:
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