Longitudinal waves

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 waves 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/transversal wave, in which the displacements of the medium are at right angles to the direction of propagation. Some transverse waves are mechanical, meaning that the wave needs a medium to travel through. Transverse mechanical waves are also called "shear waves".

By acronym, "longitudinal waves" and "transverse waves" were occasionally abbreviated by some authors as "L-waves" and "T-waves" respectively for their own convenience. While these two acronyms have specific meanings in seismology (L-wave for Love wave or long wave) and electrocardiography (see T wave), some authors chose to use "l-waves" (lowercase 'L') and "t-waves" instead, although they are not commonly found in physics writings except for some popular science books.

Longitudinal waves include sound waves (vibrations in pressure, particle of displacement, and particle velocity propagated in an elastic medium) and seismic P-waves (created by earthquakes and explosions). 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. Sound waves in air are longitudinal, pressure waves.

In the case of longitudinal harmonic sound waves, the frequency and wavelength can be described by the formula

where:

The quantity x/c is the time that the wave takes to travel the distance x.

The ordinary frequency (f) 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.

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