Longitudinal waves are waves in which the displacement of the medium is in the same direction as, or the opposite direction to, the direction of propagation of the wave. Mechanical longitudinal waves are also called compressional or compression waves, because they produce compression and rarefaction when traveling through a medium, and pressure waves, because they produce increases and decreases in pressure. The other main type of wave is the transverse wave, in which the displacements of the medium are at right angles to the direction of propagation. Transverse waves, for instance, describe some bulk sound waves in solid materials ; these are also called "shear waves" to differentiate them from the pressure waves that these materials also support. Longitudinal waves include sound waves and seismic P-waves. In longitudinal waves, the displacement of the medium is parallel to the propagation of the wave. A wave along the length of a stretched Slinky toy, where the distance between coils increases and decreases, is a good visualization, and contrasts with the standing wave along an oscillating guitar string which is transverse.
Nomenclature
"Longitudinal waves" and "transverse waves" have been abbreviated by some authors as "L-waves" and "T-waves," respectively, for their own convenience. While these two abbreviations have specific meanings in seismology and electrocardiography, some authors chose to use "l-waves" and "t-waves" instead, although they are not commonly found in physics writings except for some popular science books.
Sound waves
In the case of longitudinal harmonic sound waves, the frequency and wavelength can be described by the formula where:
y is the displacement of the point on the traveling sound wave;
x is the distance the point has traveled from the wave's source;
The quantity x/c is the time that the wave takes to travel the distance x. The ordinary frequency of the wave is given by The wavelength can be calculated as the relation between a wave's speed and ordinary frequency. For sound waves, the amplitude of the wave is the difference between the pressure of the undisturbed air and the maximum pressure caused by the wave. Sound's propagation speed depends on the type, temperature, and composition of the medium through which it propagates.
Pressure waves
The equations for sound in a fluid given above also apply to acoustic waves in an elastic solid. Although solids also support transverse waves, longitudinal sound waves in the solid exist with a velocity and wave impedance dependent on the material's density and its rigidity, the latter of which is described by the material's bulk modulus.
Electromagnetics
lead to the prediction of electromagnetic waves in a vacuum, which are strictly transverse waves, that is, the electric and magnetic fields of which the wave consists are perpendicular to the direction of the wave's propagation. However plasma waves are longitudinal inasmuch as these are not electromagnetic waves but density waves of charged particles, but which can couple to the electromagnetic field. After Heaviside's attempts to generalize Maxwell's equations, Heaviside came to the conclusion that electromagnetic waves were not to be found as longitudinal waves in "free space" or homogeneous media. Maxwell's equations, as we now understand them, retain that conclusion: in free-space or other uniform isotropic dielectrics, electro-magnetic waves are strictly transverse. However electromagnetic waves can display a longitudinal component in the electric and/or magnetic fields when traversing birefringent materials, or inhomogeneous materials especially at interfaces such as Zenneck waves. In the development of modern physics, Alexandru Proca was known for developing relativistic quantum field equations bearing his name which apply to the massive vector spin-1 mesons. In recent decades some other theorists, such as Jean-Pierre Vigier and Bo Lehnert of the Swedish Royal Society, have used the Proca equation in an attempt to demonstrate photon mass as a longitudinal electromagnetic component of Maxwell's equations, suggesting that longitudinal electromagnetic waves could exist in a Dirac polarized vacuum. However photon rest mass is strongly doubted by most physicists.
