A report on Wavelength and Wave

The wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests (on top), or troughs (on bottom), or corresponding zero crossings as shown.

Surface waves in water showing water ripples

Sinusoidal standing waves in a box that constrains the end points to be nodes will have an integer number of half wavelengths fitting in the box.

Example of biological waves expanding over the brain cortex, an example of spreading depolarizations.

A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue)

Wavelength λ, can be measured between any two corresponding points on a waveform

Wavelength is decreased in a medium with slower propagation.

Animation of two waves, the green wave moves to the right while blue wave moves to the left, the net red wave amplitude at each point is the sum of the amplitudes of the individual waves. Note that f(x,t) + g(x,t) = u(x,t)

$Refraction: upon entering a medium where its speed is lower, the wave changes direction.$

Sine, square, triangle and sawtooth waveforms.

Separation of colors by a prism (click for animation)

Amplitude modulation can be achieved through f(x,t) = 1.00×sin(2π/0.10×(x−1.00×t)) and g(x,t) = 1.00×sin(2π/0.11×(x−1.00×t))only the resultant is visible to improve clarity of waveform.

Various local wavelengths on a crest-to-crest basis in an ocean wave approaching shore

Illustration of the envelope (the slowly varying red curve) of an amplitude-modulated wave. The fast varying blue curve is the carrier wave, which is being modulated.

A sinusoidal wave travelling in a nonuniform medium, with loss

The red square moves with the phase velocity, while the green circles propagate with the group velocity

A wave on a line of atoms can be interpreted according to a variety of wavelengths.

A wave with the group and phase velocities going in different directions

Standing wave. The red dots represent the wave nodes

Wavelength of a periodic but non-sinusoidal waveform.

$Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism$

$Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction (refraction) that results.$

Pattern of light intensity on a screen for light passing through two slits. The labels on the right refer to the difference of the path lengths from the two slits, which are idealized here as point sources.

Identical waves from two sources undergoing interference. Observed at the bottom one sees 5 positions where the waves add in phase, but in between which they are out of phase and cancel.

$Diffraction pattern of a double slit has a single-slit envelope.$

Relationship between wavelength, angular wavelength, and other wave properties.

Schematic of light being dispersed by a prism. Click to see animation.

A propagating wave packet; in general, the envelope of the wave packet moves at a different speed than the constituent waves.

Animation showing the effect of a cross-polarized gravitational wave on a ring of test particles

One-dimensional standing waves; the fundamental mode and the first 5 overtones.

A two-dimensional standing wave on a disk; this is the fundamental mode.

Electromagnetic waves, according to their frequencies (or wavelengths) have more specific designations including radio waves, infrared radiation, terahertz waves, visible light, ultraviolet radiation, X-rays and gamma rays.

- Wave

Sinusoids are the simplest traveling wave solutions, and more complex solutions can be built up by superposition.

- Wavelength

7 related topics with Alpha

Frequency

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Number of occurrences of a repeating event per unit of time.

A pendulum with a period of 2.8 s and a frequency of 0.36 Hz

Diagram of the relationship between the different types of frequency and other wave properties.

Complete spectrum of electromagnetic radiation with the visible portion highlighted

The sound wave spectrum, with rough guide of some applications

For cyclical phenomena such as oscillations, waves, or for examples of simple harmonic motion, the term frequency is defined as the number of cycles or vibrations per unit of time.

For periodic waves in nondispersive media (that is, media in which the wave speed is independent of frequency), frequency has an inverse relationship to the wavelength, λ (lambda).

Electromagnetic radiation

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Shows the relative wavelengths of the electromagnetic waves of three different colours of light (blue, green, and red) with a distance scale in micrometers along the x-axis.

In electromagnetic radiation (such as microwaves from an antenna, shown here) the term "radiation" applies only to the parts of the electromagnetic field that radiate into infinite space and decrease in intensity by an inverse-square law of power, so that the total radiation energy that crosses through an imaginary spherical surface is the same, no matter how far away from the antenna the spherical surface is drawn. Electromagnetic radiation thus includes the far field part of the electromagnetic field around a transmitter. A part of the "near-field" close to the transmitter, forms part of the changing electromagnetic field, but does not count as electromagnetic radiation.

Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. The electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together.

Representation of the electric field vector of a wave of circularly polarized electromagnetic radiation.

Electromagnetic spectrum with visible light highlighted

Rough plot of Earth's atmospheric absorption and scattering (or opacity) of various wavelengths of electromagnetic radiation

In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, propagating through space, carrying electromagnetic radiant energy.

The position of an electromagnetic wave within the electromagnetic spectrum can be characterized by either its frequency of oscillation or its wavelength.

A man standing next to large ocean waves at Porto Covo, Portugal

Wind wave

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Water surface wave that occurs on the free surface of bodies of water.

The phases of an ocean surface wave: 1. Wave Crest, where the water masses of the surface layer are moving horizontally in the same direction as the propagating wavefront. 2. Falling wave. 3. Trough, where the water masses of the surface layer are moving horizontally in the opposite direction of the wavefront direction. 4. Rising wave.

NOAA ship Delaware II in bad weather on Georges Bank

Surf on a rocky irregular bottom. Porto Covo, west coast of Portugal

Classification of the spectrum of ocean waves according to wave period

Stokes drift in shallow water waves ([[:File:Shallow water wave.gif|Animation]])

Stokes drift in a deeper water wave ([[:File:Deep water wave.gif|Animation]])

Photograph of the water particle orbits under a – progressive and periodic – surface gravity wave in a wave flume. The wave conditions are: mean water depth d = 2.50 ft, wave height H = 0.339 ft, wavelength λ = 6.42 ft, period T = 1.12 s.

The image shows the global distribution of wind speed and wave height as observed by NASA's TOPEX/Poseidon's dual-frequency radar altimeter from October 3 to October 12, 1992. Simultaneous observations of wind speed and wave height are helping scientists to predict ocean waves. Wind speed is determined by the strength of the radar signal after it has bounced off the ocean surface and returned to the satellite. A calm sea serves as a good reflector and returns a strong signal; a rough sea tends to scatter the signals and returns a weak pulse. Wave height is determined by the shape of the return radar pulse.
A calm sea with low waves returns a condensed pulse whereas a rough sea with high waves returns a stretched pulse. Comparing the two images above shows a high degree of correlation between wind speed and wave height. The strongest winds (33.6 mph) and highest waves are found in the Southern Ocean. The weakest winds — shown as areas of magenta and dark blue — are generally found in the tropical oceans.

Wave length (distance from crest to crest in the direction of propagation)

Wind waves are mechanical waves that propagate along with the interface between water and air; the restoring force is provided by gravity, and so they are often referred to as surface gravity waves.

$A ray of light being refracted in a plastic block$

Refractive index

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Optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.

$A ray of light being refracted in a plastic block$

$Refraction of a light ray$

$Thomas Young coined the term index of refraction.$

$Diamonds have a very high refractive index of 2.417.$

$A split-ring resonator array arranged to produce a negative index of refraction for microwaves$

$In optical mineralogy, thin sections are used to study rocks. The method is based on the distinct refractive indices of different minerals.$

$Light of different colors has slightly different refractive indices in water and therefore shows up at different positions in the rainbow.$

$In a prism, dispersion causes different colors to refract at different angles, splitting white light into a rainbow of colors.$

$The variation of refractive index with wavelength for various glasses. The shaded zone indicates the range of visible light.$

The colors of a soap bubble are determined by the optical path length through the thin soap film in a phenomenon called thin-film interference.

$Refraction of light at the interface between two media of different refractive indices, with n2 > n1. Since the phase velocity is lower in the second medium (v2 < v1), the angle of refraction θ2 is less than the angle of incidence θ1; that is, the ray in the higher-index medium is closer to the normal.$

Total internal reflection can be seen at the air-water boundary.

$The power of a magnifying glass is determined by the shape and refractive index of the lens.$

$The relation between the refractive index and the density of silicate and borosilicate glasses$

$A calcite crystal laid upon a paper with some letters showing double refraction$

Birefringent materials can give rise to colors when placed between crossed polarizers. This is the basis for photoelasticity.

$A gradient-index lens with a parabolic variation of refractive index (n) with radial distance (x). The lens focuses light in the same way as a conventional lens.$

$The principle of many refractometers$

$A handheld refractometer used to measure the sugar content of fruits$

A differential interference contrast microscopy image of yeast cells

The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum.

It can also be applied to wave phenomena such as sound.

The interference of two waves. When in phase, the two lower waves create constructive interference (left), resulting in a wave of greater amplitude. When 180° out of phase, they create destructive interference (right).

Wave interference

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Interference of right traveling (green) and left traveling (blue) waves in Two-dimensional space, resulting in final (red) wave

Interference of waves from two point sources.

A magnified image of a coloured interference pattern in a soap film. The "black holes" are areas of almost total destructive interference (antiphase).

Geometrical arrangement for two plane wave interference

Interference fringes in overlapping plane waves

Optical interference between two point sources that have different wavelengths and separations of sources.

Creation of interference fringes by an optical flat on a reflective surface. Light rays from a monochromatic source pass through the glass and reflect off both the bottom surface of the flat and the supporting surface. The tiny gap between the surfaces means the two reflected rays have different path lengths. In addition the ray reflected from the bottom plate undergoes a 180° phase reversal. As a result, at locations (a) where the path difference is an odd multiple of λ/2, the waves reinforce. At locations (b) where the path difference is an even multiple of λ/2 the waves cancel. Since the gap between the surfaces varies slightly in width at different points, a series of alternating bright and dark bands, interference fringes, are seen.

White light interference in a soap bubble. The iridescence is due to thin-film interference.

The Very Large Array, an interferometric array formed from many smaller telescopes, like many larger radio telescopes.

In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude.

The fringe spacing increases with increase in wavelength, and with decreasing angle

US Army bombers flying over near-periodic swell in shallow water, close to the Panama coast (1933). The sharp crests and very flat troughs are characteristic for cnoidal waves.

Cnoidal wave

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A cnoidal wave, characterised by sharper crests and flatter troughs than in a sine wave. For the shown case, the elliptic parameter is m = 0.9.

Crossing swells, consisting of near-cnoidal wave trains. Photo taken from Phares des Baleines (Whale Lighthouse) at the western point of Île de Ré (Isle of Rhé), France, in the Atlantic Ocean.

Validity of several theories for periodic water waves, according to Le Méhauté (1976). The light-blue area gives the range of validity of cnoidal wave theory; light-yellow for Airy wave theory; and the dashed blue lines demarcate between the required order in Stokes' wave theory. The light-gray shading gives the range extension by numerical approximations using fifth-order stream-function theory, for high waves (H > ¼ Hbreaking).

Parameter relations for cnoidal wave solutions of the Korteweg–de Vries equation. Shown is −log10 (1−m), with m the elliptic parameter of the complete elliptic integrals, as a function of dimensionless period τ √g/h and relative wave height H / h. The values along the contour lines are −log10 (1−m), so a value 1 corresponds with m = 1 − 10−1 = 0.9 and a value 40 with m = 1 − 10−40.

Undular bore and whelps near the mouth of Araguari River in north-eastern Brazil. View is oblique toward mouth from airplane at approximately 100 ft altitude.

In fluid dynamics, a cnoidal wave is a nonlinear and exact periodic wave solution of the Korteweg–de Vries equation.

They are used to describe surface gravity waves of fairly long wavelength, as compared to the water depth.

Wavelength of a sine wave, λ, can be measured between any two consecutive points with the same phase, such as between adjacent crests, or troughs, or adjacent zero crossings with the same direction of transit, as shown.

Wave vector

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In physics, a wave vector (also spelled wavevector) is a vector which helps describe a wave.

Its magnitude is either the wavenumber or angular wavenumber of the wave (inversely proportional to the wavelength), and its direction is ordinarily the direction of wave propagation (but not always; see below).