compression wave: Definition from Answers.com

Longitudinal waves are waves that have the same direction of oscillations or vibrations along or parallel to their direction of travel, which means that the oscillations of the medium (particle) is in the same direction or opposite direction as the motion of the wave. Mechanical longitudinal waves have been also referred to as compressional waves or compression waves.

Plane pressure wave

Representation of the propagation of a longitudinal wave on a 2d grid (empirical shape)

1 Non-electromagnetic
- 1.1 Sound waves
- 1.2 Pressure waves
2 Electromagnetic
3 See also
4 References
5 Further reading
6 External links

Non-electromagnetic

Examples of longitudinal waves include sound waves (alternation in pressure, particle displacement, or particle velocity propagated in an elastic material) and seismic P-waves (created by earthquakes and explosions).

Sound waves

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

$y(x,t) = y_0 \sin\Bigg( \omega \left(t-\frac{x}{c} \right) \Bigg)$

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;
t is the time elapsed;
y₀ is the amplitude of the oscillations,
c is the speed of the wave; and
ω is the angular frequency of the wave.

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

The ordinary frequency f, in hertz, of the wave can be found using

$f = \frac{\omega}{2 \pi}.$

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 pressure of the medium through which it propagates.

Pressure waves

In an elastic medium with rigidity, a harmonic pressure wave oscillation has the form,

$y(x,t)\, = y_0 \cos(k x - \omega t +\varphi)$

where:

y₀ is the amplitude of displacement,
k is the wavenumber,
x is distance along the axis of propagation,
ω is angular frequency,
t is time, and
φ is phase difference.

The force acting to return the medium to its original position is provided by the medium's bulk modulus.^[1]

Electromagnetic

Maxwell's equations lead to the prediction of electromagnetic waves in a vacuum, which are transverse (in that the electric fields and magnetic fields vary perpendicularly to the direction of propagation).^[2] However, in a plasma or a confined space, there can exist waves which are either longitudinal or transverse, or a mixture of both.^[2]^[3] In plasma waves, there exists some examples and these plasma waves can occur in the situation of force-free magnetic fields.

In the early development of electromagnetism there was some suggesting that longitudinal electromagnetic waves existed in a vacuum. 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.^[4] But it should be stated that Maxwell's equations do lead to the appearance of longitudinal waves under some circumstances in either plasma waves or guided waves. Basically distinct from the "free-space" waves, such as those studied by Hertz in his UHF experiments, are Zenneck waves.^[5] The longitudinal mode of a resonant cavity is a particular standing wave pattern formed by waves confined in a cavity. The longitudinal modes correspond to the wavelengths of the wave which are reinforced by constructive interference after many reflections from the cavity's reflecting surfaces. Recently, Haifeng Wang et al. proposed a method that can generate longitudinal electromagnetic (light) wave in free space, and this wave can propagate without divergence for a few wavelengths.^[6]

References

^ Weisstein, Eric W., "P-Wave". Eric Weisstein's World of Science.
^ ^a ^b David J. Griffiths, Introduction to Electrodynamics, ISBN 0-13-805326-X
^ John D. Jackson, Classical Electrodynamics, ISBN 0-471-30932-X.
^ Heaviside, Oliver, "Electromagnetic theory". Appendices: D. On compressional electric or magnetic waves. Chelsea Pub Co; 3rd edition (1971) 082840237X
^ Corum, K. L., and J. F. Corum, "The Zenneck surface wave", Nikola Tesla, Lightning observations, and stationary waves, Appendix II. 1994.
^ Haifeng Wang, Luping Shi, Boris Luk'yanchuk, Colin Sheppard and Chong Tow Chong, "Creation of a needle of longitudinally polarized light in vacuum using binary optics," Nature Photonics, Vol.2, pp 501-505, 2008

External links

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		Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved. Read more
		Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Longitudinal wave". Read more

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