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A point source is a single identifiable ''localized'' source of something. A point source has a negligible extent, distinguishing it from other source geometries. Sources are called point sources because, in
mathematical model A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...
ing, these sources can usually be approximated as a mathematical point 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 is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
,
star A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...
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 Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...
. In three dimensions, the density of something leaving a point source decreases in proportion to the
inverse square In science, an inverse-square law is any scientific law stating that the observed "intensity" of a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental ca ...
of the
distance Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two co ...
from the source, if the distribution is
isotropic In physics and geometry, isotropy () is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence '' anisotropy''. ''Anisotropy'' is also ...
, and there is no absorption or other loss.


Mathematics

In mathematics, a point source is a singularity from which 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 scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
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, \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 or other small aperture, viewed from a distance much greater than the size of the hole * Light from a street light in a large-scale study of
light pollution Light pollution is the presence of any unwanted, inappropriate, or excessive artificial Visible spectrum, lighting. In a descriptive sense, the term ''light pollution'' refers to the effects of any poorly implemented lighting sources, during the ...
or street illumination


Other electromagnetic radiation

Radio wave Radio waves (formerly called Hertzian waves) are a type of electromagnetic radiation with the lowest frequencies and the longest wavelengths in the electromagnetic spectrum, typically with frequencies below 300 gigahertz (GHz) and wavelengths g ...
sources that are smaller than one radio
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
are also generally treated as point sources. Radio emissions generated by a fixed electrical circuit are usually polarized, producing
anisotropic Anisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit ver ...
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 ), is a penetrating form of electromagnetic radiation arising from high energy interactions like the radioactive decay of atomic nuclei or astronomical events like solar flares. It consists o ...
and
X-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
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, is the profession devoted to protecting people and their environment from potential radiation hazards, while making it possible to enjoy the beneficial uses of radiation. H ...
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". Exposu ...
. Examples: * Radio antennas are often smaller than one wavelength, even though they are many meters across * Pulsars are treated as point sources when observed using
radio telescopes A radio telescope is a specialized antenna (radio), antenna and radio receiver used to detect radio waves from astronomical radio sources in the sky. Radio telescopes are the main observing instrument used in radio astronomy, which studies the r ...
*In nuclear physics, a "hot spot" is a point source of
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes: * ''electromagnetic radiation'' consisting of photons, such as radio waves, microwaves, infr ...


Sound

Sound In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the br ...
is an oscillating
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
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, or sound pollution, is the propagation of noise or sound with potential harmful effects on humans and animals. The source of outdoor noise worldwide is mainly caused by machines, transport and propagation systems.Senate Publi ...
from a
jet engine A jet engine is a type of reaction engine, discharging a fast-moving jet (fluid), jet of heated gas (usually air) that generates thrust by jet propulsion. While this broad definition may include Rocket engine, rocket, Pump-jet, water jet, and ...
in a large-scale study of noise pollution * A
loudspeaker A loudspeaker (commonly referred to as a speaker or, more fully, a speaker system) is a combination of one or more speaker drivers, an enclosure, and electrical connections (possibly including a crossover network). The speaker driver is an ...
may be considered as a point source in a study of the
acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...
of
airport An airport is an aerodrome with extended facilities, mostly for commercial Aviation, air transport. They usually consist of a landing area, which comprises an aerially accessible open space including at least one operationally active surf ...
announcements A coaxial loudspeaker 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 (ionising) radiation, including Radioactive decay, nuclear radiation, consists of subatomic particles or electromagnetic waves that have enough energy per individual photon or particle to ionization, ionize atoms or molecules by detaching ...
instruments. They are usually sealed capsules and are most commonly used for gamma, x-ray and beta-measuring instruments.


Heat

In a vacuum, heat escapes as
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes: * ''electromagnetic radiation'' consisting of photons, such as radio waves, microwaves, infr ...
isotropically. If the source remains stationary in a compressible fluid such as
air An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosph ...
, flow patterns can form around the source due to
convection Convection is single or Multiphase flow, multiphase fluid flow that occurs Spontaneous process, spontaneously through the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoy ...
, leading to an
anisotropic Anisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit ver ...
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. Thermal pollution is the rise or drop in the temperature of a natural body of water caused by h ...
tracking.


Fluid

Fluid point sources are commonly used in
fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...
and
aerodynamics Aerodynamics () is the study of the motion of atmosphere of Earth, air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an ...
. 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 behavior such as is seen in vortices (for example water running into a plug-hole or
tornado A tornado is a violently rotating column of air that is in contact with the surface of Earth and a cumulonimbus cloud or, in rare cases, the base of a cumulus cloud. It is often referred to as a twister, whirlwind or cyclone, although the ...
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 of Earth, air that are harmful to humans, other living beings or the environment. Pollutants can be Gas, gases like Ground-level ozone, ozone or nitrogen oxides or small particles li ...
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 electricity generation, generation of electric power. Power stations are generally connected to an electr ...
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 vertical pipe, channel or similar structure through which flue gases are exhausted to the outside air. Flue gases are produced when coal, oi ...
in a large-scale analysis of air pollution *
Water pollution Water pollution (or aquatic pollution) is the contamination of Body of water, water bodies, with a negative impact on their uses. It is usually a result of human activities. Water bodies include lakes, rivers, oceans, aquifers, reservoirs and ...
from an
oil refinery An oil refinery or petroleum refinery is an industrial processes, industrial process Factory, plant where petroleum (crude oil) is transformed and refining, refined into products such as gasoline (petrol), diesel fuel, Bitumen, asphalt base, ...
wastewater Wastewater (or waste water) is water generated after the use of freshwater, raw water, drinking water or saline water in a variety of deliberate applications or processes. Another definition of wastewater is "Used water from any combination of do ...
discharge outlet in a large-scale analysis of water pollution * Gas escaping from a pressurized pipe in a laboratory * Smoke is often released from point sources in a
wind tunnel A wind tunnel is "an apparatus for producing a controlled stream of air for conducting aerodynamic experiments". The experiment is conducted in the test section of the wind tunnel and a complete tunnel configuration includes air ducting to and f ...
in order to create a plume of smoke which highlights the flow of the wind over an object * Smoke from a localized 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 *
Dirac delta function In mathematical analysis, the Dirac delta function (or distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line ...


References

{{reflist Experimental physics Mathematical physics