Point source

For other uses, seePoint source (disambiguation).

Apoint sourceis a single identifiablelocalisedsource of something. A point source has negligible extent, distinguishing it from other source geometries. Sources are called point sources because inmathematical modeling,these sources can usually be approximated as a mathematicalpointto simplify analysis.

The actual source need not be physically small, if its size is negligible relative to other length scales in the problem. For example, inastronomy,starsare routinely treated as point sources, even though they are in actuality much larger than theEarth.

Inthree dimensions,the density of something leaving a point source decreases in proportion to theinverse squareof thedistancefrom the source, if the distribution isisotropic,and there is noabsorptionor other loss.

Mathematics

In mathematics, apoint sourceis asingularityfrom whichfluxor flow is emanating. Although singularities such as this do not exist in the observable universe, mathematical point sources are often used as approximations to reality inphysicsand other fields.

Visible electromagnetic radiation (light)

Generally, asource of lightcan be considered a point source if the resolution of the imaging instrument is too low to resolve the source's apparent size. There are two types and sources of light: a point source and an extended source.

Mathematically an object may be considered a point source if itsangular size,$\theta$,is much smaller than the resolving power of the telescope:
$\theta <<\lambda /D$,
where$\lambda$is the wavelength of light and$D$is the telescope diameter.

Examples:

• Light from a distant star seen through a small telescope
• Light passing through apinholeor other smallaperture,viewed from a distance much greater than the size of the hole
• Light from astreet lightin a large-scale study oflight pollutionor streetillumination

Other electromagnetic radiation

Radio wavesources which are smaller than one radiowavelengthare also generally treated as point sources. Radio emissions generated by a fixed electrical circuit are usuallypolarized,producinganisotropicradiation. If the propagating medium is lossless, however, the radiant power in the radio waves at a given distance will still vary as the inverse square of the distance if the angle remains constant to the source polarization.

Gamma rayandX-raysources may be treated as a point source if sufficiently small.Radiological contaminationand nuclear sources are often point sources. This has significance inhealth physicsandradiation protection.

Examples:

• Radio antennasare often smaller than one wavelength, even though they are many metres across
• Pulsarsare treated as point sources when observed usingradio telescopes
• In nuclear physics, a "hot spot" is a point source ofradiation

Sound

Soundis an oscillatingpressurewave. As the pressure oscillates up and down, an audio point source acts in turn as a fluid point source and then a fluid point sink. (Such an object does not exist physically, but is often a good simplified model for calculations.)

Examples:

• Seismic vibrationfrom a localised seismic experiment searching for oil
• Noise pollutionfrom ajet enginein a large-scale study of noise pollution
• Aloudspeakermay be considered as a point source in a study of theacousticsofairportannouncements

Acoaxial loudspeakeris designed to work as a point source to allow a wider field for listening.

Ionizing radiation

Geiger-Müller counterwith dual counts/dose rate display measuring a "point source".

Point sources are used as a means of calibratingionizing radiationinstruments. They are usually a sealed capsule and are most commonly used for gamma, x-ray and beta measuring instruments.

Heat

Amushroom cloudas an example of a thermal plume. A nuclear explosion can be treated as a thermal point source in large-scale atmospheric simulations.

Invacuum,heat escapes asradiationisotropically. If the source remains stationary in acompressible fluidsuch asair,flow patterns can form around the source due toconvection,leading to ananisotropicpattern of heat loss. The most common form of anisotropy is the formation of a thermalplumeabove the heat source. Examples:

• Geological hotspots on the surface of the Earth which lie at the tops of thermal plumes rising from deep inside the Earth
• Plumes of heat studied inthermal pollutiontracking.

Fluid

Fluid point sources are commonly used influid dynamicsandaerodynamics.A point source of fluid is the inverse of a fluid point sink (a point where fluid is removed). Whereas fluid sinks exhibit complex rapidly changing behaviour such as is seen invortices(for example water running into a plug-hole ortornadoesgenerated at points where air is rising), fluid sources generally produce simple flow patterns, with stationary isotropic point sources generating an expanding sphere of new fluid. If the fluid is moving (such as wind in air or currents in water) aplumeis generated from the point source.

Examples:

• Air pollutionfrom apower plantflue gas stackin a large scale analysis of air pollution
• Water pollutionfrom anoil refinerywastewaterdischarge outlet in a large scale analysis of water pollution
• Gas escaping from a pressurised pipe in a laboratory
• Smoke is often released from point sources in awind tunnelin order to create aplumeof smoke which highlights the flow of the wind over an object
• Smoke from a localised chemical fire can be blown in the wind to form aplumeof pollution

Pollution

Main article:Point source pollution

Sources of various types of pollution are often considered as point sources in large-scale studies of pollution.

See also

• Line source
• Dirac delta function