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| '''Longitudinal waves''', also known as "l-waves", are [[wave]]s in which the displacement of the medium is in the same direction as, or the opposite direction to, the direction of travel 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. 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 mechanical waves are also called "t-waves" or "shear waves".
| | It can be non-spherical as per the shape of gutters. In his chest is the Autobot Matrix, also known as the Creation Matrix, which is carried by each Autobot leader and passed down as time goes on. Beginning repairs on a roof without this inspection and estimate will make the job far more difficult. A watertight cap all over the roof would trap moisture resulting in mold and rot. Â If your roof leak repair needs to be made where two surfaces meet, such as, at a chimney or vent then you need to look for breaks in the caulking or flashing. <br><br>This ensures that the kids are in good hands should something go wrong. Tualatin Roofing Contractors That Offer Guarantees. So don't wait any longer and get yourself the benefit of these awesome quality and extremely reliable contractors. Cleaning out gutters and removing rubbish can [http://content.yudu.com/Library/A2yifr/ABackgroundInImmedia/resources/index.htm?referrerUrl=http%3A%2F%2Ffree.yudu.com%2Fitem%2Fdetails%2F2061490%2FA-Background-In-Immediate-Products-For--Best-Roofe ,arlington roofer,] avoid these costs and the potential need for a new roof. However, there is one disadvantage of metal roofing, and that is corrosion. <br><br>This will prevent future problems and ensure your home maintains its maximum value. Not only is it great for RV roof leaks repair, it is also going to save you quite a bit of time and money, since you do not have to take the RV in to a professional to fix. Mild to severe tornados pass through Georgia every year. They may consider adding additional maintenance fees in order to cover their expenses. Fort Worth epdm roofing, ([http://roofrepairftworth.jimdo.com/ http://roofrepairftworth.jimdo.com/]) Optimus sent the Autobots after the humans, and he himself intercepted the vehicle they were in. <br><br>Hire Slate roofing contractors Maryland for slate roof repair MD and get your roof cleaned and replaced at an [http://www.wikipedia.org/wiki/attractive+view attractive view] and affordable cost. roof, and recommend preventative measures to avoid. typically present other important information the assessment district has readily available. Once the moss is scrubbed off, a strip of zinc or copper should be nailed to the affected area. Most of the roof contractors UK are very eager to provide the best quality output to their clients. <br><br>Water can travel significantly along the insides of the house before it finally creates the tell-tale stain. By spending a [https://foursquare.com/user/92515187/list/fort-worth-roofing-contractors Fort Worth epdm roofing,] bit more money you can be sure that the job will be done properly and last another five to ten years. Cedar's insulative quality, artistic appeal, and wind and shock resistance makes the cedar shakes and shingle the best choice for your roofing. Screw the wire brush cleaning head onto the first rod, and push the head upwards through the inspection hatch while rotating the rod counterclockwise. Hot air flows out, while cool air from the outside flows in. |
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| [[Image:Onde compression impulsion 1d 30 petit.gif|thumb|305px|Plane pressure pulse wave]]
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| [[Image:Ondes compression 2d 20 petit.gif|thumb|305px|Representation of the propagation of an omnidirectional pulse wave on a 2d grid (empirical shape)]]
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| ==Examples==
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| Longitudinal waves include sound waves ([[vibration]]s in pressure, particle displacement, and particle velocity propagated in an [[elasticity (physics)|elastic]] medium) and seismic [[P-wave]]s (created by earthquakes and explosions).
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| 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.
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| ===Sound waves===
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| In the case of longitudinal harmonic sound waves, the [[frequency]] and [[wavelength]] can be described by the formula
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| :<math>y(x,t) = y_0 \cos \Bigg( \omega \left(t-\frac{x}{c} \right) \Bigg)</math>
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| where:
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| * ''y'' is the displacement of the point on the traveling sound wave;
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| * ''x'' is the distance the point has traveled from the wave's source;
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| * ''t'' is the time elapsed;
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| * ''y''<sub>0</sub> is the amplitude of the oscillations,
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| * ''c'' is the speed of the wave; and
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| * ''ω'' is the angular frequency of the wave.
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| The quantity ''x''/''c'' is the time that the wave takes to travel the distance ''x''.
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| The ordinary frequency (''f'') of the wave is given by
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| :<math> f = \frac{\omega}{2 \pi}.</math>
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| 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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| Sound's [[Speed_of_sound|propagation speed]] depends on the type, temperature, and composition of the medium through which it propagates.
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| ===Pressure waves===
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| In an elastic medium with [[Stiffness|rigidity]], a harmonic pressure wave oscillation has the form,
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| :<math>y(x,t)\, = y_0 \cos(k x - \omega t +\varphi)</math>
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| where:
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| * ''y''<sub>0</sub> is the amplitude of displacement,
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| * ''k'' is the [[wavenumber]],
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| * ''x'' is the distance along the axis of propagation,
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| * ''ω'' is the angular frequency,
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| * ''t'' is the time, and
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| * ''φ'' is the phase difference.
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| The restoring force, which acts to return the medium to its original position, is provided by the medium's [[bulk modulus]].<ref>Weisstein, Eric W., "''[http://scienceworld.wolfram.com/physics/P-Wave.html P-Wave]''". Eric Weisstein's World of Science.</ref>
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| ==Electromagnetic== | |
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| [[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).<ref name="griffiths">David J. Griffiths, Introduction to Electrodynamics, ISBN 0-13-805326-X</ref> However, waves can exist in plasmas or confined spaces, called [[plasma wave]]s, which can be longitudinal, transverse, or a mixture of both.<ref name="griffiths" /><ref>John D. Jackson, Classical Electrodynamics, ISBN 0-471-30932-X.</ref> Plasma waves can also occur in force-free magnetic fields{{citation needed|date=September 2012}}.
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| In the early development of electromagnetism, there were some like [[Alexandru Proca]] (1897-1955) known for developing relativistic quantum field equations bearing his name (Proca's equations) for the massive, vector spin-1 mesons. In recent decades some extended electromagnetic 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>Lakes, R. (1998). Experimental limits on the photon mass and cosmic magnetic vector potential. Physical review letters, 80(9), 1826-1829</ref> as a longitudinal electromagnetic component of Maxwell's equations, suggesting that longitudinal electromagnetic waves could exist in a Dirac polarized vacuum.
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| 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.<ref>Heaviside, Oliver, "''Electromagnetic theory''". ''Appendices: D. On compressional electric or magnetic waves''. Chelsea Pub Co; 3rd edition (1971) 082840237X</ref> But Maxwell's equations do lead to the appearance of longitudinal waves under some circumstances, for example, in [[plasma waves]] or [[wave guide|guided waves]]. Basically distinct from the "free-space" waves, such as those studied by Hertz in his UHF experiments, are [[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> The longitudinal modes of a [[resonant cavity]] are the particular standing wave patterns formed by waves confined in a cavity. The longitudinal modes correspond to those 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 a longitudinal electromagnetic (light) wave in free space, and this wave can propagate without divergence for a few wavelengths.<ref>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, [http://dx.doi.org/10.1038/nphoton.2008.127 doi:10.1038/nphoton.2008.127]</ref>
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| ==See also==
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| * [[Transverse wave]]
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| * [[Shear wave splitting]]
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| * [[Transverse mode]]
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| ==References==
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| {{reflist}}
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| ==Further reading==
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| * Varadan, V. K., and 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.
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| * 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.
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| * Krishan, S, and A A Selim, "''[http://www.iop.org/EJ/abstract/0032-1028/10/10/305 Generation of transverse waves by non-linear wave-wave interaction]''". Department of Physics, University of Alberta, Edmonton, Canada.
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| * Barrow, W. L., "''Transmission of electromagnetic waves in hollow tubes of metal''", [[Proc. IRE]], vol. 24, pp. 1298–1398, October 1936.
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| * Russell, Dan, "''[http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html Longitudinal and Transverse Wave Motion]''". Acoustics Animations, Kettering University Applied Physics.
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| * Longitudinal Waves, with animations "''[http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/u11l1b.html The Physics Classroom]''"
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| ==External links==
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| *[http://www.phy.hk/wiki/englishhtm/Lwave.htm An interactive simulation of longitudinal travelling wave]
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| *[http://www.acoustics.salford.ac.uk/feschools/waves/wavetypes.htm Wave types explained using high speed film and animations]
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| [[Category:Wave mechanics]]
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| [[Category:Waves]]
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| [[Category:Articles containing video clips]]
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It can be non-spherical as per the shape of gutters. In his chest is the Autobot Matrix, also known as the Creation Matrix, which is carried by each Autobot leader and passed down as time goes on. Beginning repairs on a roof without this inspection and estimate will make the job far more difficult. A watertight cap all over the roof would trap moisture resulting in mold and rot. Â If your roof leak repair needs to be made where two surfaces meet, such as, at a chimney or vent then you need to look for breaks in the caulking or flashing.
This ensures that the kids are in good hands should something go wrong. Tualatin Roofing Contractors That Offer Guarantees. So don't wait any longer and get yourself the benefit of these awesome quality and extremely reliable contractors. Cleaning out gutters and removing rubbish can ,arlington roofer, avoid these costs and the potential need for a new roof. However, there is one disadvantage of metal roofing, and that is corrosion.
This will prevent future problems and ensure your home maintains its maximum value. Not only is it great for RV roof leaks repair, it is also going to save you quite a bit of time and money, since you do not have to take the RV in to a professional to fix. Mild to severe tornados pass through Georgia every year. They may consider adding additional maintenance fees in order to cover their expenses. Fort Worth epdm roofing, (http://roofrepairftworth.jimdo.com/) Optimus sent the Autobots after the humans, and he himself intercepted the vehicle they were in.
Hire Slate roofing contractors Maryland for slate roof repair MD and get your roof cleaned and replaced at an attractive view and affordable cost. roof, and recommend preventative measures to avoid. typically present other important information the assessment district has readily available. Once the moss is scrubbed off, a strip of zinc or copper should be nailed to the affected area. Most of the roof contractors UK are very eager to provide the best quality output to their clients.
Water can travel significantly along the insides of the house before it finally creates the tell-tale stain. By spending a Fort Worth epdm roofing, bit more money you can be sure that the job will be done properly and last another five to ten years. Cedar's insulative quality, artistic appeal, and wind and shock resistance makes the cedar shakes and shingle the best choice for your roofing. Screw the wire brush cleaning head onto the first rod, and push the head upwards through the inspection hatch while rotating the rod counterclockwise. Hot air flows out, while cool air from the outside flows in.