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Topic: Plane waves

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	Plane Waves
		The wave vector is normal to the wave fronts and its length is the wavenumber.
		A plane wave in two or three dimensions is like a sine wave in one dimension except that crests and troughs aren't points, but form lines (2-D) or planes (3-D) perpendicular to the direction of wave propagation.
		The large arrow is a vector called the wave vector, which defines (1) the direction of wave propagation by its orientation perpendicular to the wave fronts, and (2) the wavenumber by its length.
	www.physics.nmt.edu /~raymond/classes/ph13xbook/node22.html (536 words)

	Method and apparatus for generating periodic structures in substrates by synthetic wavelength holograph exposure - ...
		Plane wave vectors k1 and k3 are incident on the surface 10 at angles of incidence,.theta.
		Plane wave vectors k2 and k4 are incident on the surface 10 at angles of incidence,.phi.
		Plane wave k1 reflects off of the reflective surface 18 of the mirror 14 to form plane wave k3 which is incident on the photo-sensitive material 11 at an angle of incidence -.theta.
	www.freepatentsonline.com /6709790.html (3871 words)

	Plane Waves (Sound)
		One of the remarkable characteristics of the plane wave solution of the non-linear equations is that the harmonic distortion grows as the wave propagates.
		It is neglected in the derivation of the linearized wave equations.
		For a light wave the ratio of energy carried by the wave divided by the wave momentum is equal to the speed of light.
	www.silcom.com /~aludwig/Physics/Main/Plane_waves.html (2196 words)

	Sound Waves
		By a plane wave, we mean one in which quantities vary only with the distance along a certain direction, and of course with the time.
		A plane wave propagating in a thermally stratified atmosphere can be represented by a ray normal to the wave front whose inclination to the horizontal changes so that the velocity with which the line of intersection of the wave front with a horizontal plane moves, called the trace velocity, is constant.
		Just as in the case of the refracted wave, the wavefront must also have a constant phase relation to the incident wave, and so its trace must be the same as the traces of the incident and refracted waves, and move with the same trace velocity.
	www.du.edu /~jcalvert/waves/soundwav.htm (9029 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: )
		Longitudinal waves such as sound waves do not exhibit polarization, because for these waves the direction of oscillation is along the direction of travel.
		The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation to most light waves (a plane wave is a wave with infinitely long and wide wavefronts).
		All electromagnetic waves propagating in free space or in a uniform material of infinite extent have electric and magnetic fields perpendicular to the direction of propagation.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Polarization (4461 words)

	Electromagnetic Waves and Antennas
		The propagation, reflection, and transmission of plane waves, and the analysis and design of multilayer films.
		For example, the mathematical techniques for analyzing wave propagation in multilayer structures, multisegment transmission lines, and the design of multilayer optical filters are the same as those used in DSP, such as the lattice structures of linear prediction, the analysis and synthesis of speech, and geophysical signal processing.
		Uniform plane waves in lossless media, monochromatic waves, wave impedance, polarization, waves in lossy media, waves in weakly lossy dielectrics, propagation in good conductors, propagation in oblique directions, complex waves, Doppler effect.
	www.ece.rutgers.edu /~orfanidi/ewa (2045 words)

	Plane waves and polarization
		A plane wave is a wave in which the disturbance is constant in planes perpendicular to the direction of motion of the wave, which we shall always take to be along the x axis in these notes.
		In a string, for example, the direction of the motion associated with the wave is up-and-down along the y-axis, whereas the direction of motion of the wave is along the x-axis.
		In this case, the direction of motion of the disturbance and of the propagation of the wave are parallel, a special situation defined as longitudinal polarization.
	people.ccmr.cornell.edu /~muchomas/P214/Notes/OtherWaves/node6.html (337 words)

	CiteULike: Propagation of plane waves in a pre-stressed elastic medium (Site not responding. Last check: )
		Propagation of plane waves in a pre-stressed elastic medium
		The propagation of plane waves in such a medium is discussed.
		It is shown that pure longitudinal and shear waves can propagate only in certain specific directions which are defined.
	www.citeulike.org /user/Andrew_Norris/article/805581 (206 words)

	X-Plane, by Austin Meyer
		Here is how this works: In the (real) Viggen, the plane flies it's approach to land at such a high angle of attack (because it has low-aspect ratio delta wings and lands on very short fields) that the nose is way up and the velocity vector is way down in the HUD.
		Tailwheel-equipped planes will follow your commanded tailwheel deflection tightly, rather than wandering around based on their ground-track, simulating the pilot holding the pedals tensely under his feet with no slop at all, making the tail-wheel planes a lot more stable.
		Well, advanced planes have multiple buses, with each bus powering half the stuff in the plane.
	www.x-plane.com (2473 words)

	Reflection of Spherical or Plane Waves
		When a spreading spherical wave reaches a wall or other obstacle, it is either reflected or scattered.
		A wave is scattered when it encounters a surface which has variations on the scale of the spatial wavelength.
		As a general rule, reverberation should be diffuse in order to avoid ``standing waves'' (isolated energetic modes).
	ccrma.stanford.edu /~jos/pasp/Reflection_Spherical_or_Plane.html (341 words)

	plane waves
		We are asked to substitute a plane wave solution into the TDSE for V=0 and show that it satisfies the TDSE (this is straightforward).
		Yes, in general plane waves are only solutions of the Schrodinger equation in regions where the potential is constant.
		The plane waves are states of definite momenta, but you know that in the presence of a non-constant potential, the momentum will change, therefore these states can't have definite energy (they can't be energy eigenstates) when the potential varies with position.
	www.physicsforums.com /showthread.php?t=104353 (280 words)

	Plane waves in three dimensions
		In this chapter we seek a deeper understanding of plane waves in three dimensions, where the examples and theory typically refer to functions of time t and two space coordinates (x,y), or to 3-D migration images where the t coordinate is depth or traveltime depth.
		In this chapter we will see that the wave model implies the 3-D whitener is not a cube filter but two planar filters.
		The wave model allows us to determine the scale factor of a signal, even where signals fluctuate in strength because of interference.
	sepftp.stanford.edu /sep/prof/gee/lmn/paper_html/node1.html (140 words)

	:: POLYTECHNIC UNIVERSITY :: Department of Electrical and Computer Engineering
		Electromagnetic wave propagation in free space and in dielectrics is studied starting from a consideration of distributed inductance and capacitance on transmission lines.
		Electromagnetic plane waves are obtained as a special case.
		Snell`s law and the reflection and transmission coefficients at dielectric interfaces are derived for obliquely propagation plane waves.
	www.poly.edu /ece/undergraduate/courses/ee3604/index.php (124 words)

	Properties of Acoustic Plane Wave
		The wavelength is directly proportional to the velocity of the wave and inversely proportional to the frequency of the wave.
		The direction of wave propagation is from left to right and the movement of the lines indicate the direction of particle oscillation.
		The values for the wavelength, frequency, and wave velocity can be adjusted in the dialog boxes to see their effects on the wave.
	www.ndt-ed.org /EducationResources/CommunityCollege/Ultrasonics/Physics/acousticplane.htm (286 words)

	Savage Earth: Restless Planet
		But when a fault is stuck, the rocks on either side of it store the building stresses until a critical limit is reached, and the rocks move suddenly along the fault, releasing the stresses like a spring uncoiling.
		Body waves travel outward in all directions, including downward, from the quake's focus -- that is, the particular spot where the fault first began to rupture.
		Surface waves, by contrast, are confined to the upper few hundred miles of the crust.
	www.pbs.org /wnet/savageearth/earthquakes (1193 words)

	Plane Waves
		The wave vector is normal to the wave fronts and its length is the wavenumber.
		A plane wave in two or three dimensions is like a sine wave in one dimension except that crests and troughs aren't points, but form lines (2-D) or planes (3-D) perpendicular to the direction of wave propagation.
		The large arrow is a vector called the wave vector, which defines (1) the direction of wave propagation by its orientation perpendicular to the wave fronts, and (2) the wavenumber by its length.
	kestrel.nmt.edu /~raymond/classes/ph13xbook/node22.html (536 words)

	AES Abstract
		Spiral waves are a basic feature of nature and have been observed in a variety of biological systems, but spiral dynamics have not been studied in mammalian cortex.
		The oscillations were organized spatiotemporally as propagating waves, and complex wave patterns such as spiral, plane, ring and irregular waves were observed both in slices and in vivo.
		We examined the initiation of spiral waves in slices and found that collision of two wave fronts usually occurred prior to the initiation of spiral waves.
	www.aesnet.org /Visitors/AnnualMeeting/Abstractsnew/dsp_Abstract.cfm?id=664 (381 words)

	Abstract
		In this paper (Part 1), the qP, qSV and SH plane waves, propagating in the plane of symmetry of anisotropic viscoelastic media, are studied as functions of propagation direction N and the inhomogeneity parameter D from (-infinity, +infinity).
		For inhomogeneous plane waves, D is not equal 0, and for homogeneous plane waves, D equals 0.
		Similarly, the modulus of the attenuation vector of an inhomogeneous plane wave may be lower than that for the relevant homogeneous plane wave.
	sw3d.mff.cuni.cz /papers/r14vc1.htm (623 words)

	Physics Today June 2001
		The plane along which failure occurs is called the fault plane and the point where failure initiates is called the focus.
		Seismic waves radiated during earthquakes provide evidence that the properties on a fault plane are indeed complex.
		Short-period seismic waves seen on seismograms and felt by people are generally believed to be caused by a fractal distribution of small fault-slip zones, each zone radiating short-period waves.
	www.aip.org /pt/vol-54/iss-6/p34.html (3433 words)

	University of Bath - Programme & Unit Catalogues 2006/07
		After completion of this unit students should be able to determine the propagation constants for waves on TEM transmission lines using circuit concepts and to illustrate the fields occurring in the simple transmission modes for parallel conductors and coaxial lines.
		Students should also be able to apply solutions of the EM wave equation for plane waves to propagation in dielectric and conducting media.
		Propagation of plane waves, Huygens wavelets; qualitative illustration of diffraction.
	www.bath.ac.uk /catalogues/2006-2007/ee/ee20090.htm (397 words)

	Intrinsic Local Modes in 1-D Lattices, Coexistence of ILM and Plane Waves (Site not responding. Last check: )
		When the eigenvector of the odd-parity anharmonic local mode is excited on top of a background of small amplitude random displacements, the resultant power spectrum is shown in the lower panel of the Figure.
		The local mode peak is clearly separated from the plane wave spectrum, and the number of plane wave peaks is decreased from 10 to 9.
		Note that the frequencies of the plane waves shown in the lower panel have shifted slightly to higher frequencies, but are still confined to the phonon band of the harmonic spectrum as expected from Rayleigh theorem[1].
	www.lassp.cornell.edu /~sievers/ilm/ilm1d/ilmplane.html (373 words)

	Abstract (Site not responding. Last check: )
		The reflection/transmission laws of plane waves at a plane interface between two homogeneous anisotropic viscoelastic (dissipative) halfspaces are discussed.
		Algorithms for determining the slowness vectors of reflected/transmitted plane waves from the known slowness vector of the incident wave are proposed.
		The proposed algorithms may be applied to bulk plane waves (A=0), homogeneous plane waves (P and A parallel), and inhomogeneous plane waves (P and A non-parallel).
	sw3d.mff.cuni.cz /papers/r14vc3.htm (219 words)

	Longitudinal and Transverse Wave Motion (Site not responding. Last check: )
		Mechanical Waves are waves which propagate through a material medium (solid, liquid, or gas) at a wave speed which depends on the elastic and inertial properties of that medium.
		In a longitudinal wave the particle displacement is parallel to the direction of wave propagation.
		The wave is seen as the motion of the compressed region (ie, it is a pressure wave), which moves from left to right.
	www.kettering.edu /~drussell/Demos/waves/wavemotion.html (528 words)

	Reflection and Refraction of Plane Waves (Site not responding. Last check: )
		Reflection and refraction of an arbitrary electromagnetic wave at a plane interf...
		Abstract: Reflection and refraction of an arbitrary electromagnetic wave at a pl...
		Reflection and refraction of electromagnetic waves by the plane boundary of a no...
	www.scienceoxygen.com /electrical/166.html (133 words)

	Scientific American Mind: Train Your Brain -- Mental exercises with neurofeedback may ease symptoms of ...
		He found a previously unknown pattern of brain waves with frequencies between 12 and 15 hertz (Hz), or cycles per second, in a part of the brain called the sensorimotor cortex.
		Frequencies around 10 Hz, known as alpha waves, are present in a relaxed but awake brain; they emerge, for example, when we lie back with our eyes closed.
		Theta waves, with high amplitudes and frequencies falling between those of delta and alpha waves, normally appear in adults during light sleep and meditation.
	www.sciammind.com /article.cfm?articleID=000C075D-4357-13D9-810183414B7F0000 (799 words)

	Theory of Meteor Reflection \| International Meteor Organization
		Radio waves are in fact scattered from all parts of a meteor trail, but constructive interference only occurs in given directions, along the paths considered in geometrical optics.
		In the beginning of trail diffusion, there is a moment where a resonance effect occurs in the reflection of radio waves with an electric vector perpendicular to the trail direction.
		The distance at which these radio waves can be received strongly depends on the strength of the spark, the shielding of the device, the position of the device in the antenna radiation pattern,...
	www.imo.net /radio/reflection.html (2548 words)

	"SM51C-1418" in fm06 (Site not responding. Last check: )
		It is found that the nonlinear evolution of the K-H instability depends on the fast-mode Mach number of the surface wave obtained in the plasma rest frame.
		When the fast- mode Mach number on either side of the surface wave is greater than 1, the surface disturbances associated with the K-H instability can generate fast-mode nonlinear plane waves on that side of the TD.
		For the high-Mach-number K-H instability, a huge amount of the energy is transported away from the velocity shear layer with the expanding of the nonlinear plane waves.
	www.agu.org /cgi-bin/wais?hh=SM51C-1418 (295 words)

	Plane Wave Method
		This technique expands the periodic structure into a superposition of plane waves with known coefficients and periodic field distribution (periodic structures will cause periodic field distributions) which are going to be solved into a superposition of plane waves with unknown coefficients, where is the number of plane waves used in the expansions.
		By solving this eigenvalue problem, the frequencies corresponding to each plane wave (which provides dispersion relationship of the periodic structure) and, i.e., the periodic field distributions, can be obtained.
		However, for 3D problems, an impractically tremendous number of plane waves may be needed to ensure accuracy.
	www.eecis.udel.edu /~dprather/research/pwm.shtml (169 words)

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