A longitudinal wave has an oscillating displacement parallel to the direction of propagation. An acoustic wave in a fluid supplies a familiar example.
A compressional wave is a longitudinal wave whose propagation produces changes of volume or density. In an isotropic elastic solid its displacement is parallel to the wavevector; substituting that polarization into the dynamic Navier-Cauchy equation gives the displayed speed. In a fluid without static shear stiffness the analogous speed is , with the appropriate compressional bulk modulus. Reflection at a rigid elastic boundary can convert part of its energy into a shear wave.
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A longitudinal wave is a type of wave in which the particles of the medium through which the wave travels vibrate in the same direction as the wave's propagation. In other words, the displacement of the medium's particles is parallel to the direction of the wave's energy transfer. This is in contrast to transverse waves, where the displacement of the medium's particles is perpendicular to the direction of the wave's travel. A common example of a longitudinal wave is a sound wave.