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A point source is a single identifiable ''localised'' source of something. A point source has negligible extent, distinguishing it from other source geometries. Sources are called point sources because in mathematical modeling, these sources can usually be approximated as a mathematical
point Point or points may refer to: Places * Point, LewisImage:Point Western Isles NASA World Wind.png, Satellite image of Point Point ( gd, An Rubha), also known as the Eye Peninsula, is a peninsula some 11 km long in the Outer Hebrides (or Western I ...
to 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, in
astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses mathematics, phys ...
,
star A star is an astronomical object consisting of a luminous spheroid of plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral) or heliotrope, a mineral aggregate * Quark ...

star
s are routinely treated as point sources, even though they are in actuality much larger than the
Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distribution on Earth, covered wi ...

Earth
. In
three dimensions Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Greek language, Ancient Greek wikt:παρά#Ancient Greek, παρά, ''par ...
, the density of something leaving a point source decreases in proportion to the
inverse square Image:Inverse square law.svg, 420px, S represents the light source, while r represents the measured points. The lines represent the flux emanating from the sources and fluxes. The total number of flux lines depends on the strength of the light so ...
of the
distance Distance is a numerical measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or eve ...

distance
from the source, if the distribution is
isotropic Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, "equal") and ''tropos'' (τρόπος, "way"). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by ...
, and there is no
absorption Absorption may refer to: Chemistry and biology *Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials *Absorption (skin), a route by which substances enter the body through the skin *Absorption (pharmacolo ...
or other loss.


Mathematics

In mathematics, a point source is a
singularity Singularity or singular point may refer to: Science, technology, and mathematics Mathematics * Mathematical singularity, a point at which a given mathematical object is not defined or not "well-behaved", for example infinite or not differentiabl ...
from which
flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...

flux
or 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 in
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scie ...

physics
and other fields.


Visible electromagnetic radiation (light)

Generally, a source of light can 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 its
angular size The angular diameter, angular size, apparent diameter, or apparent size is an angular distance describing how large a sphere of a sphere A sphere (from Greek language, Greek —, "globe, ball") is a Geometry, geometrical object in solid geometr ...

angular 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 a
pinhole A hole is an opening in or through a particular medium, usually a solid body. Holes occur through natural and artificial processes, and may be useful for various purposes, or may represent a problem needing to be addressed in many fields of engin ...

pinhole
or other small
aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of ray (optics), rays that come to a focus (optics), focus ...

aperture
, viewed from a distance much greater than the size of the hole * Light from a
street light A street light, light pole, lamppost, street lamp, light standard, or lamp standard is a raised source of light on the edge of a road or path. Similar lights may be found on a railway platform A railway platform is an area alongside a railwa ...

street light
in a large-scale study of
light pollution Light pollution is the presence of unwanted, inappropriate, or excessive artificial lighting Lighting or illumination is the deliberate use of light Light or visible light is electromagnetic radiation within the portion of the elect ...

light pollution
or street
illumination
illumination


Other electromagnetic radiation

Radio wave Radio waves are a type of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies ma ...
sources which are smaller than one radio
wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

wavelength
are also generally treated as point sources. Radio emissions generated by a fixed electrical circuit are usually polarized, producing
anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions as opposed to isotropy Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, ...
radiation. 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 ray A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, it ...
and
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Moti ...

X-ray
sources may be treated as a point source if sufficiently small. Radiological contamination and nuclear sources are often point sources. This has significance in
health physics Health physics, also referred to as the science of radiation protection Radiation protection, also known as radiological protection, is defined by the International Atomic Energy Agency The International Atomic Energy Agency (IAEA) is an in ...
and
radiation protection Radiation protection, also known as radiological protection, is defined by the International Atomic Energy Agency (IAEA) as "The protection of people from harmful effects of exposure to ionizing radiation, and the means for achieving this". Exposur ...
. Examples: * Radio antennas are often smaller than one wavelength, even though they are many metres across *
Pulsars Animation of a rotating pulsar. The sphere in the middle represents the neutron star, the curves indicate the magnetic field lines and the protruding cones represent the emission zones. A pulsar (from ''pulse'' and ''-ar'' as in “quasar A ...
are treated as point sources when observed using
radio telescopes A radio telescope is a specialized antenna Antenna (pl. antennas or antennae) may refer to: Science and engineering * Antenna (radio) In radio engineering, an antenna or aerial is the interface between radio waves propagating through sp ...

radio telescopes
*In nuclear physics, a "hot spot" is a point source of
radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and f ...

radiation


Sound

Sound In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

Sound
is an oscillating
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

pressure
wave. 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 vibration from a localised seismic experiment searching for oil *
Noise pollution Noise pollution, also known as or sound , is the propagation of noise with ranging impacts on the activity of human or animal life, most of them harmful to a degree. The source of outdoor noise worldwide is mainly caused by machines, transport, ...
from a
jet engine A jet engine is a type of reaction engine A reaction engine is an engine or motor that produces thrust by expelling reaction mass, in accordance with Newton's third law of motion. This law of motion is most commonly paraphrased as: "For ...

jet engine
in a large-scale study of noise pollution * A
loudspeaker A loudspeaker (or ''speaker driver'', or most frequently just ''speaker'') is an Acoustical engineering#Electroacoustics, electroacoustic transducer, that is, a device that converts an electrical audio signal into a corresponding sound. A ''spe ...

loudspeaker
may be considered as a point source in a study of the
acoustics Acoustics is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other wo ...
of
airport An airport is an aerodrome An aerodrome (Commonwealth English The use of the English language English is a West Germanic languages, West Germanic language first spoken in History of Anglo-Saxon England, early medieval En ...

airport
announcements A
coaxial loudspeakerA coaxial loudspeaker is a loudspeaker system in which the individual driver units radiate sound from the same point or axis. Two general types exist: one is a compact design using two or three speaker drivers, usually in car audio, and the other is ...
is designed to work as a point source to allow a wider field for listening.


Ionizing radiation

Point sources are used as a means of calibrating
ionizing radiation Ionizing radiation (or ionising radiation), including nuclear radiation, consists of s or s that have sufficient to s or s by detaching s from them. The particles generally travel at a speed that is greater than 1% of , and the electromagnetic w ...
instruments. They are usually a sealed capsule and are most commonly used for gamma, x-ray and beta measuring instruments.


Heat

In
vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Gree ...

vacuum
, heat escapes as
radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and f ...

radiation
isotropically. If the source remains stationary in a
compressible fluid Compressible flow (or gas dynamics) is the branch of fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objec ...
such as
air File:Atmosphere gas proportions.svg, Composition of Earth's atmosphere by volume, excluding water vapor. Lower pie represents trace gases that together compose about 0.043391% of the atmosphere (0.04402961% at April 2019 concentration ). Number ...

air
, flow patterns can form around the source due to
convection Convection is single or multiphase fluid flow that occurs Spontaneous process, spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When t ...

convection
, leading to an
anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions as opposed to isotropy Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, ...
pattern of heat loss. The most common form of anisotropy is the formation of a thermal plume above 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 in
thermal pollution Thermal pollution, sometimes called "thermal enrichment," is the degradation of water quality by any process that changes ambient water temperature Temperature is a physical quantity that expresses hot and cold. It is the manifestation of ...
tracking.


Fluid

Fluid point sources are commonly used in
fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...
and
aerodynamics Aerodynamics, from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appr ...
. 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 in
vortices , revealed by colored smoke In fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the ...

vortices
(for example water running into a plug-hole or
tornado A tornado is a violently rotating column of air File:Atmosphere gas proportions.svg, Composition of Earth's atmosphere by volume, excluding water vapor. Lower pie represents trace gases that together compose about 0.043391% of the atmos ...

tornado
es generated 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) a plume is generated from the point source. Examples: *
Air pollution Air pollution is the presence of substances in the atmosphere that are harmful to the health of humans and other Outline of life forms, living beings, or cause damage to the climate or to materials. There are different types of air pollutants, ...

Air pollution
from a
power plant A power station, also referred to as a power plant and sometimes generating station or generating plant, is an industrial facility for the generation A generation is "all of the people born and living Living or The Living may refer to: ...

power plant
flue gas stack A flue-gas stack, also known as a smoke stack, chimney stack or simply as a stack, is a type of chimney A chimney is an architectural ventilation structure made of masonry, clay or metal that isolates hot toxic exhaust gas Exhaust gas o ...
in a large scale analysis of air pollution *
Water pollution Water pollution (or aquatic pollution) is the contamination of water bodies ( Lysefjord) in Norway Norway ( nb, ; nn, ; se, Norga; smj, Vuodna; sma, Nöörje), officially the Kingdom of Norway, is a Nordic countries, Nordic c ...

Water pollution
from an
oil refinery An oil refinery or petroleum refinery is an industrial process Industrial processes are procedures involving chemical A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some referen ...
wastewater Wastewater is generated after the use of fresh water Water (chemical formula H2O) is an , transparent, tasteless, odorless, and , which is the main constituent of 's and the s of all known living organisms (in which it acts as a ). It i ...

wastewater
discharge 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 a
wind tunnel Wind tunnels are large tubes with air blowing through them which are used to replicate the interaction between air and an object flying through the air or moving along the ground. Researchers use wind tunnels to learn more about how an aircraft ...

wind tunnel
in order to create a plume of 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 a plume of pollution


Pollution

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


See also

*
Line source A line source, as opposed to a point source, area source, or Volume source (pollution), volume source, is a source of air, noise, water contamination or electromagnetic radiation that emanates from a linear (one-dimensional) geometry. The most ...
*
Dirac delta function In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is n ...


References

{{reflist Experimental physics Mathematical physics