Wavelength

[1][2] In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings.

[6] Wavelength depends on the medium (for example, vacuum, air, or water) that a wave travels through.

A sound wave is a variation in air pressure, while in light and other electromagnetic radiation the strength of the electric and the magnetic field vary.

In linear media, any wave pattern can be described in terms of the independent propagation of sinusoidal components.

Thus the wavelength of a 100 MHz electromagnetic (radio) wave is about: 3×108 m/s divided by 108 Hz = 3 m. The wavelength of visible light ranges from deep red, roughly 700 nm, to violet, roughly 400 nm (for other examples, see electromagnetic spectrum).

The wavelengths of sound frequencies audible to the human ear (20 Hz–20 kHz) are thus between approximately 17 m and 17 mm, respectively.

For example, the speed of light can be determined from observation of standing waves in a metal box containing an ideal vacuum.

The first form, using reciprocal wavelength in the phase, does not generalize as easily to a wave in an arbitrary direction.

Generalizations to sinusoids of other phases, and to complex exponentials, are also common; see plane wave.

[9] For electromagnetic waves, this change in the angle of propagation is governed by Snell's law.

The mathematical relationship that describes how the speed of light within a medium varies with wavelength is known as a dispersion relation.

In addition, the method computes a slowly changing amplitude to satisfy other constraints of the equations or of the physical system, such as for conservation of energy in the wave.

Waves in crystalline solids are not continuous, because they are composed of vibrations of discrete particles arranged in a regular lattice.

This produces aliasing because the same vibration can be considered to have a variety of different wavelengths, as shown in the figure.

[14] This indeterminacy in wavelength in solids is important in the analysis of wave phenomena such as energy bands and lattice vibrations.

In the special case of dispersion-free and uniform media, waves other than sinusoids propagate with unchanging shape and constant velocity.

[17] Large-amplitude ocean waves with certain shapes can propagate unchanged, because of properties of the nonlinear surface-wave medium.

[24] Louis de Broglie postulated that all particles with a specific value of momentum p have a wavelength λ = h/p, where h is the Planck constant.

For example, the electrons in a CRT display have a De Broglie wavelength of about 10−13 m. To prevent the wave function for such a particle being spread over all space, de Broglie proposed using wave packets to represent particles that are localized in space.

[25] The spatial spread of the wave packet, and the spread of the wavenumbers of sinusoids that make up the packet, correspond to the uncertainties in the particle's position and momentum, the product of which is bounded by Heisenberg uncertainty principle.

[29] The notion of path difference and constructive or destructive interference used above for the double-slit experiment applies as well to the display of a single slit of light intercepted on a screen.

The main result of this interference is to spread out the light from the narrow slit into a broader image on the screen.

Diffraction is the fundamental limitation on the resolving power of optical instruments, such as telescopes (including radiotelescopes) and microscopes.

[32] The resolvable spatial size of objects viewed through a microscope is limited according to the Rayleigh criterion, the radius to the first null of the Airy disk, to a size proportional to the wavelength of the light used, and depending on the numerical aperture:[33] where the numerical aperture is defined as

Such structures have applications in extraordinary optical transmission, and zero-mode waveguides, among other areas of photonics.

It is equal to the ordinary wavelength reduced by a factor of 2π (ƛ = λ/2π), with SI units of meter per radian.