In a transverse wave, vibrations are perpendicular to the direction of the wave motion. In a longitudinal wave, vibrations are parallel to the direction of the wave motion.
In the transverse wave, crest and trough are the parts of a wave. The crest is a part where the displacement is maximum. While the trough is the part where the displacement is minimum.
In the longitudinal wave, the compression and the rarefaction are the part of a wave. In compression, the particles are very close to each other. While, in rarefaction, the particles are far apart.
