Editing Longitudinal wave

{{Short description|Type of wave}}
{{Redirect|Pressure wave|seismic pressure waves specifically|P wave}}
[[File:Onde compression impulsion 1d 30 petit.gif|thumb|305px|alt=Graph depicting a planar wave moving left-to-right|A type of longitudinal wave: A plane pressure pulse wave.]]

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'''Longitudinal waves''' are [[wave]]s which [[Oscillation|oscillate]] in the direction which is parallel to the direction in which the wave travels and displacement of the medium is in the same (or opposite) direction of the [[wave propagation]]. [[Mechanical wave|Mechanical]] longitudinal waves are also called ''compressional'' or '''compression waves''', because they produce [[compression (physics)|compression]] and [[rarefaction]] when travelling through a medium, and '''pressure waves''', because they produce increases and decreases in [[pressure]]. A wave along the length of a stretched [[Slinky]] toy, where the distance between coils increases and decreases, is a good visualization. Real-world examples include sound waves (vibrations in pressure, a particle of displacement, and particle velocity propagated in an [[elasticity (physics)|elastic]] medium) and seismic [[P wave]]s (created by earthquakes and explosions).

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 (but not in [[fluid]]s); these are also called "[[Shearing (physics)|shear]] waves" to differentiate them from the (longitudinal) pressure waves that these materials also support.

== Nomenclature ==
"Longitudinal waves" and "transverse waves" have been abbreviated by some authors as "L-waves" and "T-waves", respectively, for their own convenience.<ref>
{{cite book
 |first=Erhard |last=Winkler
 |year=1997
 |title=Stone in Architecture: Properties, durability
 |publisher=Springer Science & Business Media
 |url=https://books.google.com/books?id=u9zt12_gE-AC
 |via=Google books
 |pages=[https://books.google.com/books?id=u9zt12_gE-AC&pg=PA55 55], [https://books.google.com/books?id=u9zt12_gE-AC&pg=PA57 57]
}}
</ref>
While these two abbreviations have specific meanings in [[seismology]] (L-wave for [[Love wave]]<ref>
{{cite book
 |first=M. |last=Allaby |author-link=Michael Allaby
 |year=2008
 |title=A Dictionary of Earth Sciences |edition=3rd
 |publisher=Oxford University Press
 |url=http://www.oxfordreference.com/oso/viewentry/10.1093$002facref$002f9780199211944.001.0001$002facref-9780199211944-e-4890;jsessionid=ECBC0E5982D11489C3ACF1C7F4D391F9
 |via=oxfordreference.com
}}</ref> or long wave<ref>
{{cite book
 |first1=Dean A. |last1=Stahl
 |first2=Karen   |last2=Landen
 |year=2001
 |title=Abbreviations Dictionary   |edition=10th
 |publisher=[[CRC Press]]
 |page=618
 |url=https://books.google.com/books?id=t3fLBQAAQBAJ&pg=PA618
 |via=Google books
}}
</ref>) 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.<ref>
{{cite book
 |first=Francine |last=Milford
 |year=2016
 |title=The Tuning Fork
 |pages=43–44
 |url=https://books.google.com/books?id=SK3QDQAAQBAJ&pg=PA43
}}
</ref>

== Sound waves ==
{{further|Acoustic theory}}
For longitudinal harmonic sound waves, the [[frequency]] and [[wavelength]] can be described by the formula

:<math>\ y(x,t) = y_\mathsf{o}\cdot\cos\!\Bigl(\ \omega\cdot\left( t - \tfrac{\ x\ }{ c } \right)\ \Bigr)\ </math>

where:
: <math>\ y\ ~~</math>  is the displacement of the point on the traveling sound wave;[[File:Ondes compression 2d 20 petit.gif|thumb|305px|alt=Graph depicting a symmetrical wave spreading outwards from the center in all directions|Representation of the propagation of an omnidirectional pulse wave on a 2‑D&nbsp;grid (empirical shape)]]
: <math>\ x\ ~~</math>  is the distance from the point to the wave's source;
: <math>\ t\ ~~</math>  is the time elapsed;
: <math>\ y_\mathsf{o}\ </math>  is the [[amplitude]] of the oscillations,
: <math>\ c\ ~~</math>  is the speed of the wave; and
: <math>\ \omega ~~</math>  is the [[angular frequency]] of the wave.

The quantity <math>\ \frac{\ x\ }{ c }\ </math> is the time that the wave takes to travel the distance <math>\ x ~.</math>

The ordinary frequency (<math>\ f\ </math>) of the wave is given by

:<math> f = \frac{ \omega }{\ 2 \pi\ } ~.</math>

The wavelength can be calculated as the relation between a wave's speed and ordinary frequency.

:<math> \lambda =\frac{ c }{\ f\ } ~.</math>

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 [[Speed of sound|propagation speed]] depends on the type, temperature, and composition of the medium through which it propagates.

== Speed of longitudinal waves ==

=== Isotropic medium ===
For [[isotropy|isotropic]] solids and liquids, the speed of a longitudinal wave can be described by
: <math>\ v_\ell = \sqrt{ \frac{~ E_\ell\ }{ \rho }\ }\ </math>
where
: <math>\ E_\ell\ ~~</math> is the [[elastic modulus]], such that <math>\ E_\ell = K_b + \frac{\ 4G\ }{ 3 }\ </math>
::: where <math>\ G\ ~~</math> is the [[shear modulus]] and <math>\ K_b\ </math> is the [[bulk modulus]];
: <math>\ \rho ~~~</math> is the mass [[density]] of the medium.

== Attenuation of longitudinal waves ==
The [[attenuation]] of a wave in a medium describes the loss of energy a wave carries as it propagates throughout the medium.<ref name=":0">{{Cite web |title=Attenuation |url=https://wiki.seg.org/wiki/Attenuation#:~:text=Attenuation%20%E2%80%94%20the%20falloff%20of%20a,which%20is%20the%20conversion%20of |website=SEG Wiki}}</ref> This is caused by the scattering of the wave at interfaces, the loss of energy due to the friction between molecules, or geometric divergence.<ref name=":0" /> The study of attenuation of elastic waves in materials has increased in recent years, particularly within the study of polycrystalline materials where researchers aim to "nondestructively evaluate the degree of damage of engineering components" and to "develop improved procedures for characterizing microstructures" according to a research team led by R. Bruce Thompson in a ''[[Wave Motion (journal)|Wave Motion]]'' publication.<ref>{{Cite journal |last1=Thompson |first1=R. Bruce |last2=Margetan |first2=F.J. |last3=Haldipur |first3=P. |last4=Yu |first4=L. |last5=Li |first5=A. |last6=Panetta |first6=P. |last7=Wasan |first7=H. |date=April 2008 |title=Scattering of elastic waves in simple and complex polycrystals |url=https://doi.org/10.1016/j.wavemoti.2007.09.008 |journal=Wave Motion |volume=45 |issue=5 |pages=655–674 |doi=10.1016/j.wavemoti.2007.09.008 |bibcode=2008WaMot..45..655T |issn=0165-2125|url-access=subscription }}</ref>

=== Attenuation in viscoelastic materials ===
In [[viscoelastic]] materials, the attenuation coefficients per length  <math>\ \alpha_\ell\ </math> for longitudinal waves and <math>\ \alpha_T\ </math> for transverse waves must satisfy the following ratio:

:<math>\ \frac{~\ \alpha_\ell\ }{~\ \alpha_T\ } ~\geq~ \frac{~ 4\ c_T^3\ }{~ 3\ c_\ell^3\ }\ </math>

where <math>\ c_T\ </math> and <math>\ c_\ell\ </math> are the transverse and longitudinal wave speeds respectively.<ref>
{{cite journal
 |last=Norris |first=Andrew N.
 |year=2017
 |title=An inequality for longitudinal and transverse wave attenuation coefficients
 |journal=The Journal of the Acoustical Society of America
 |volume=141  |issue=1  |pages=475–479
 |doi=10.1121/1.4974152  |pmid=28147617  |issn=0001-4966
 |arxiv=1605.04326   |bibcode=2017ASAJ..141..475N
 |url=https://pubs.aip.org/jasa/article/141/1/475/1058243/An-inequality-for-longitudinal-and-transverse-wave
 |via=pubs.aip.org/jasa  |lang=en
}}
</ref>

=== Attenuation in polycrystalline materials ===
Polycrystalline materials are made up of various crystal [[Grain boundary#:~:text=In materials science, a grain,thermal conductivity of the material.|grains]] which form the bulk material. Due to the difference in crystal structure and properties of these grains, when a wave propagating through a poly-crystal crosses a grain boundary, a [[scattering]] event occurs causing scattering based attenuation of the wave.<ref name=":1">{{Cite journal |last1=Kube |first1=Christopher M. |last2=Norris |first2=Andrew N. |date=2017-04-01 |title=Bounds on the longitudinal and shear wave attenuation ratio of polycrystalline materials |url=https://pubs.aip.org/jasa/article/141/4/2633/1059148/Bounds-on-the-longitudinal-and-shear-wave |journal=The Journal of the Acoustical Society of America |language=en |volume=141 |issue=4 |pages=2633–2636 |doi=10.1121/1.4979980 |pmid=28464650 |bibcode=2017ASAJ..141.2633K |issn=0001-4966|url-access=subscription }}</ref> Additionally it has been shown that the ratio rule for viscoelastic materials,
:<math>\frac{~\ \alpha_\ell\ }{~\ \alpha_T\ } ~\geq~ \frac{~ 4\ c_T^3\ }{~ 3\ c_\ell^3\ }
</math>
applies equally successfully to polycrystalline materials.<ref name=":1" />

A current prediction for modeling attenuation of waves in polycrystalline materials with elongated grains is the second-order approximation (SOA) model which accounts the second order of inhomogeneity allowing for the consideration multiple scattering in the crystal system.<ref name=":2">{{Cite journal |last1=Huang |first1=M. |last2=Sha |first2=G. |last3=Huthwaite |first3=P. |last4=Rokhlin |first4=S. I. |last5=Lowe |first5=M. J. S. |date=2021-04-01 |title=Longitudinal wave attenuation in polycrystals with elongated grains: 3D numerical and analytical modeling  |journal=The Journal of the Acoustical Society of America |language=en |volume=149 |issue=4 |pages=2377–2394 |doi=10.1121/10.0003955 |pmid=33940885 |bibcode=2021ASAJ..149.2377H |issn=0001-4966|doi-access=free }}</ref><ref>{{Cite journal |last1=Huang |first1=M. |last2=Sha |first2=G. |last3=Huthwaite |first3=P. |last4=Rokhlin |first4=S. I. |last5=Lowe |first5=M. J. S. |date=2020-12-01 |title=Elastic wave velocity dispersion in polycrystals with elongated grains: Theoretical and numerical analysis |url=https://pubs.aip.org/jasa/article/148/6/3645/1056424/Elastic-wave-velocity-dispersion-in-polycrystals |journal=The Journal of the Acoustical Society of America |language=en |volume=148 |issue=6 |pages=3645–3662 |doi=10.1121/10.0002916 |pmid=33379920 |bibcode=2020ASAJ..148.3645H |issn=0001-4966|doi-access=free |hdl=10044/1/85906 |hdl-access=free }}</ref> This model predicts that the shape of the grains in a poly-crystal has little effect on attenuation.<ref name=":2" />

== 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 (known as [[S-waves]] in [[seismology]]), longitudinal sound waves in the solid exist with a [[Speed of sound|velocity]] and [[Acoustic impedance|wave impedance]] dependent on the material's [[density]] and its [[Stiffness|rigidity]], the latter of which is described (as with sound in a gas) by the material's [[bulk modulus]].<ref>Weisstein, Eric W., "''[http://scienceworld.wolfram.com/physics/P-Wave.html P-Wave]''". Eric Weisstein's World of Science.</ref>

In May 2022, NASA reported the [[sonification]] (converting astronomical data associated with pressure waves into [[sound]]) of the black hole at the center of the [[Perseus Cluster|Perseus galaxy cluster]].<ref name="NASA-20220504">{{cite news |last1=Watzke |first1=Megan |last2=Porter |first2=Molly |last3=Mohon |first3=Lee |title=New NASA Black Hole Sonifications with a Remix |url=https://www.nasa.gov/mission_pages/chandra/news/new-nasa-black-hole-sonifications-with-a-remix.html |date=4 May 2022 |work=[[NASA]] |accessdate=11 May 2022 }}</ref><ref name="NYT-20220507">{{cite news |last=Overbye |first=Dennis |authorlink=Dennis Overbye |title=Hear the Weird Sounds of a Black Hole Singing – As part of an effort to "sonify" the cosmos, researchers have converted the pressure waves from a black hole into an audible … something.|url=https://www.nytimes.com/2022/05/07/science/space/astronomy-black-hole-sound.html  |date=7 May 2022 |work=[[The New York Times]] |accessdate=11 May 2022 }}</ref>

== Electromagnetics ==

[[Maxwell's equations]] lead to the prediction of [[electromagnetic wave]]s in a vacuum, which are strictly [[transverse wave]]s; due to the fact that they would need particles to vibrate upon, the electric and magnetic fields of which the wave consists are perpendicular to the direction of the wave's propagation.<ref name="griffiths">[[David J. Griffiths]], Introduction to Electrodynamics, {{ISBN|0-13-805326-X}}</ref> However [[plasma wave]]s are longitudinal since these are not electromagnetic waves but density waves of charged particles, but which can couple to the electromagnetic field.<ref name="griffiths" /><ref>John D. Jackson, Classical Electrodynamics, {{ISBN|0-471-30932-X}}.</ref><ref>Gerald E. Marsh (1996), Force-free Magnetic Fields, World Scientific, {{ISBN|981-02-2497-4}}</ref>

After [[Heaviside]]'s attempts to generalize Maxwell's equations, Heaviside concluded that electromagnetic waves were not to be found as longitudinal waves in "''[[free space]]''" or homogeneous media.<ref>Heaviside, Oliver, "''Electromagnetic theory''". ''Appendices: D. On compressional electric or magnetic waves''. Chelsea Pub Co; 3rd edition (1971) 082840237X</ref> 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 (surface waves for instance) such as [[Zenneck wave]]s.<ref>Corum, K. L., and J. F. Corum, "''The Zenneck surface wave''", ''Nikola Tesla, Lightning Observations, and stationary waves, Appendix II''. 1994.</ref>

In the development of modern physics, [[Alexandru Proca]] (1897–1955) was known for developing relativistic quantum field equations bearing his name (Proca's equations) 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<ref>{{Cite journal |doi = 10.1103/PhysRevLett.80.1826|bibcode = 1998PhRvL..80.1826L|title = Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential|year = 1998|last1 = Lakes|first1 = Roderic|journal = Physical Review Letters|volume = 80|issue = 9|pages = 1826–1829}}</ref> as a longitudinal electromagnetic component of Maxwell's equations, suggesting that longitudinal electromagnetic waves could exist in a Dirac polarized vacuum. However [[Photon#Experimental checks on photon mass|photon rest mass]] is strongly doubted by almost all physicists and is incompatible with the [[Standard Model]] of physics.{{cn|date=May 2021}}

== See also ==
* [[Transverse wave]]
* [[Sound]]
* [[Acoustic wave]]
* [[P-wave]]
* [[Plasma waves]]

== References ==
{{reflist}}

== Further reading ==
* Varadan, V. K., and [[Vasundara Varadan|Vasundara V. Varadan]], "''Elastic wave scattering and propagation''". ''Attenuation due to scattering of ultrasonic compressional waves in granular media'' – A.J. Devaney, H. Levine, and T. Plona. Ann Arbor, Mich., Ann Arbor Science, 1982.
* Schaaf, John van der, Jaap C. Schouten, and Cor M. van den Bleek, "''Experimental Observation of Pressure Waves in Gas-Solids Fluidized Beds''". American Institute of Chemical Engineers. New York, N.Y., 1997.
* {{cite journal |doi=10.1088/0032-1028/10/10/305|bibcode=1968PlPh...10..931K|title=Generation of transverse waves by non-linear wave-wave interaction|year=1968|last1=Krishan|first1=S.|last2=Selim|first2=A. A.|journal=Plasma Physics|volume=10|issue=10|pages=931–937}}
* {{cite journal |doi=10.1109/JRPROC.1936.227357|title=Transmission of Electromagnetic Waves in Hollow Tubes of Metal|year=1936|last1=Barrow|first1=W.L.|journal=Proceedings of the IRE|volume=24|issue=10|pages=1298–1328| s2cid=32056359 }}
* Russell, Dan, "''Longitudinal and Transverse Wave Motion''". Acoustics Animations, Pennsylvania State University, Graduate Program in Acoustics.
* Longitudinal Waves, with animations "''The Physics Classroom''"

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