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A longitudinal wave is a wave in which the particles of the wave vibrate/oscillate in the same direction as the direction of propagation of the wave.
They are formed by alternate compressions and rarefactions in the wave medium. There is an increase in pressure at the compressions and a decrease in pressure at the rarefactions. Hence, they are also called pressure.
A sound wave is an example of a longitudinal wave.
(check the related link for an illustration)
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