Editing Transverse wave (section)

=== Circular polarization === 
If the medium is linear and allows multiple independent displacement directions for the same travel direction <math>\widehat{d}</math>, we can choose two mutually perpendicular directions of polarization, and express any wave linearly polarized in any other direction as a linear combination (mixing) of those two waves.

By combining two waves with same frequency, velocity, and direction of travel, but with different phases and independent displacement directions, one obtains a [[circular polarization|circularly]] or [[elliptical polarization|elliptically polarized]] wave.  In such a wave the particles describe circular or elliptical trajectories, instead of moving back and forth.

It may help understanding to revisit the thought experiment with a taut string mentioned above. Notice that you can also launch waves on the string by moving your hand to the right and left instead of up and down. This is an important point. There are two independent (orthogonal) directions that the waves can move. (This is true for any two directions at right angles, up and down and right and left are chosen for clarity.) Any waves launched by moving your hand in a straight line are linearly polarized waves.

But now imagine moving your hand in a circle. Your motion will launch a spiral wave on the string. You are moving your hand simultaneously both up and down and side to side. The maxima of the side to side motion occur a quarter wavelength (or a quarter of a way around the circle, that is 90 degrees or π/2 radians) from the maxima of the up and down motion. At any point along the string, the displacement of the string will describe the same circle as your hand, but delayed by the propagation speed of the wave. Notice also that you can choose to move your hand in a clockwise circle or a counter-clockwise circle. These alternate circular motions produce right and left circularly polarized waves.

To the extent your circle is imperfect, a regular motion will describe an ellipse, and produce elliptically polarized waves. At the extreme of eccentricity your ellipse will become a straight line, producing linear polarization along the major axis of the ellipse. An elliptical motion can always be decomposed into two orthogonal linear motions of unequal amplitude and 90 degrees out of phase, with circular polarization being the special case where the two linear motions have the same amplitude.

[[File:Polarizacio.jpg|thumb|upright=1.25|Circular polarization mechanically generated on a rubber thread, converted to linear polarization by a mechanical polarizing filter.]]
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==Mechanical transverse waves==
The compressional wave speed is related to the bulk elasticity modulus of the medium while the shear wave speed is related to the shear elasticity modulus.

===Strings===

===Membranes===

===Solids===

==Electromagnetic waves== 
Electromagnetic waves behave in this same way. Electromagnetic waves are also two-dimensional transverse waves. 
Transverse waves are waves that travel perpendicular to the direction of the vibration.
Ray theory does not describe phenomena such as interference and diffraction, which require wave theory (involving the phase of the wave).
You can think of a [[Ray (optics)|ray of light]], in [[optics]], as an idealized narrow beam of electromagnetic radiation. Rays are used to model the propagation of [[light]] through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of [[Ray tracing (physics)|ray tracing]]. <ref name=zmx1>{{cite web  |url=http://kb-en.radiantzemax.com/Knowledgebase/What-is-a-ray  |title=What is a ray?  |first=Ken  |last=Moore  |date=2005-07-25  |work=ZEMAX Users' Knowledge Base  |access-date=2008-05-30  |url-status=dead  |archive-url=https://archive.today/20130624192746/http://kb-en.radiantzemax.com/Knowledgebase/What-is-a-ray  |archive-date=2013-06-24  }}</ref>            
A light ray is a line or curve that is perpendicular to the light's wavefronts (and is therefore collinear with the wave vector). Light rays bend at the interface between two dissimilar media and may be curved in a medium in which the [[refractive index]] changes. Geometric optics describes how rays propagate through an optical system.<ref name=zmx1>{{cite web  |url=http://kb-en.radiantzemax.com/Knowledgebase/What-is-a-ray  |title=What is a ray?  |first=Ken  |last=Moore  |date=2005-07-25  |work=ZEMAX Users' Knowledge Base  |access-date=2008-05-30  |url-status=dead  |archive-url=https://archive.today/20130624192746/http://kb-en.radiantzemax.com/Knowledgebase/What-is-a-ray  |archive-date=2013-06-24  }}</ref>

This two-dimensional nature should not be confused with the two components of an electromagnetic wave, the electric and magnetic field components, which are shown in the light wave diagram here. Each of these fields, the electric and the magnetic, exhibits two-dimensional transverse wave behavior, just like the waves on a string.-->
<!--MATERIAL FROM [[shear waves]] before redirection -- probably already all in [[elastography]]:
In soft biological tissues the bulk modulus varies no more than 10% while variation of the shear elasticity modulus may be several orders of magnitude depending on the structure and state of tissue.<ref>Sarvazyan AP, Skovoroda AR, Emelianov SY, Fowlkes JB, Pipe JG, Adler RS, Buxton RB, Carson PL. Biophysical bases of elasticity imaging. In: Acoustical Imaging. Ed. Jones JP, Plenum Press, New York and London, 1995; 21: 223-240.</ref><ref>Sarvazyan AP, Urban MW, Greenleaf JF. Acoustic waves in medical imaging and diagnostics. Ultrasound Med Biol. 2013 Jul;39(7):1133-46. {{doi|10.1016/j.ultrasmedbio.2013.02.006}}. Epub 2013 Apr 30. Review. {{PMID|23643056}}</ref>

==Shear Waves in Elastography==
The bulk modulus is defined by short range molecular interaction forces and depends mainly on molecular composition of tissue which is typically 75% water with little variation. In contrast to that, the shear modulus is defined by long range interactions and is highly sensitive to structural changes.  The wide range of variability makes the shear elasticity modulus and, respectively, the shear wave speed, highly sensitive to physiological and pathological structural changes of tissue. For this reason, the use of shear waves in new diagnostic methods and devices has been extensively investigated over the last two decades. Numerous new methods were developed most notable of which are [[Shear Wave Elasticity Imaging]] (SWEI), [[Magnetic Resonance Elastography]] (MRE), Supersonic Shear Imaging  (SSI), Shearwave Dispersion Ultrasound Vibrometry (SDUV), Harmonic Motion Imaging (HMI), Comb-push Ultrasound Shear Elastography (CUSE), and Spatially Modulated Ultrasound Radiation Force (SMURF).<ref>Sarvazyan AP, Rudenko OV, Swanson SD, Fowlkes JB, and Emelianov SY, Shear wave elasticity imaging: a new ultrasonic technology of medical diagnostics. Ultrasound Med. Biol. 1998; 24: 1419-35.</ref><ref>Muthupillai R, Lomas DJ, Rossman PJ, Greenleaf JF, Manduca A, and Ehman RL, Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. Science 1995; 269: 1854-7.</ref><ref>Bercoff J, Tanter M, and Fink M, Supersonic shear imaging: a new technique for soft tissue elasticity mapping. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2004; 51: 396-409.</ref><ref>Chen S, Urban MW, Pislaru C, Kinnick R, Zheng Y, Yao A, and Greenleaf JF, Shearwave dispersion ultrasound vibrometry (SDUV) for measuring tissue elasticity and viscosity. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2009; 56: 55-6.</ref><ref>Vappou J, Maleke C, and Konofagou EE, Quantitative viscoelastic parameters measured by harmonic motion imaging. Phys. Med. Biol. 2009; 54: 3579-3594.</ref><ref>Song P, Zhao H, Manduca A, Urban M W, Greenleaf J F, and Chen S, "Comb-push ultrasound shear elastography (CUSE): a novel method for two-dimensional shear elasticity imaging of soft tissues," IEEE Trans. Med. Imaging, vol. 31, pp. 1821-1832, 2012.</ref><ref>9.	McAleavey S. A., Menon M., and Orszulak J., "Shear-modulus estimation by application of spatially-modulated impulsive acoustic radiation force," Ultrason. Imaging, vol. 29, pp. 87-104, 2007.</ref>
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