It is a kind of wave motion in which the individual particles of a medium execute periodic motion about their mean position along the direction of propagation of the wave.
The sound wave is an example of longitudinal waves.
A longitudinal wave moves by the phenomena of compression and rarefaction in the medium.
In compression, the distance between any two consecutive particles of medium is less than their normal distance. Therefore, density is more than the normal density.
In a rarefaction, the distance between any two consecutive particles of medium is more than the normal distance, therefore, density is less than the normal density.
Distance between two consecutive compressions or rarefactions is equal to the wavelength of the wave. Longitudinal waves can propagate through any state of matter.