In the

physical sciences Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "physical sciences". Definition Phy ...

, the term ''spectrum'' was introduced first into

optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...

in the 17th century, referring to the range of colors observed when white light was dispersed through a

prism Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentary ...

. Soon the term referred to a plot of light

intensity Intensity may refer to: In colloquial use *Strength (disambiguation) *Amplitude * Level (disambiguation) * Magnitude (disambiguation) In physical sciences Physics *Intensity (physics), power per unit area (W/m2) *Field strength of electric, ma ...

power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...

as a function of

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...

, also known as a ''

spectral density The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, o ...

plot''. Later it expanded to apply to other

wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...

s, such as

sound wave 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 ...

s and

sea wave In fluid dynamics, a wind wave, water wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result from the wind blowing over the water surface. The contact distance in the direction o ...

s that could also be measured as a function of frequency (e.g.,

noise spectrum In audio engineering, electronics, physics, and many other fields, the color of noise or noise spectrum refers to the power spectrum of a noise signal (a signal produced by a stochastic process). Different colors of noise have significantly ...

sea wave spectrum In fluid dynamics, a wind wave, water wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result from the wind blowing over the water surface. The contact distance in the direction of t ...

). It has also been expanded to more abstract "signals", whose

power spectrum The power spectrum S_(f) of a time series x(t) describes the distribution of Power (physics), power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discre ...

can be analyzed and processed. The term now applies to any signal that can be measured or decomposed along a continuous variable, such as energy in

electron spectroscopy Electron spectroscopy refers to a group formed by techniques based on the analysis of the energies of emitted electrons such as photoelectrons and Auger electrons. This group includes X-ray photoelectron spectroscopy (XPS), which also known as Ele ...

or mass-to-charge ratio in

mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a ''mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is use ...

. Spectrum is also used to refer to a graphical representation of the signal as a function of the dependent variable.

Electromagnetic spectrum

Electromagnetic spectrum refers to the full range of all frequencies of

electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...

and also to the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object. Devices used to measure an electromagnetic spectrum are called

spectrograph An optical spectrometer (spectrophotometer, spectrograph or spectroscope) is an instrument used to measure properties of light over a specific portion of the electromagnetic spectrum, typically used in spectroscopic analysis to identify mate ...

spectrometer A spectrometer () is a scientific instrument used to separate and measure spectral components of a physical phenomenon. Spectrometer is a broad term often used to describe instruments that measure a continuous variable of a phenomenon where the ...

. The

visible spectrum The visible spectrum is the portion of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye wil ...

is the part of the electromagnetic spectrum that can be seen by the

human eye The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm. ...

. The wavelength of visible light ranges from 390 to 700 nm. The

absorption spectrum Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy, i.e., photons, from the radiating f ...

of a

chemical element A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...

chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element ...

is the spectrum of frequencies or wavelengths of incident radiation that are absorbed by the compound due to electron transitions from a lower to a higher energy state. The

emission spectrum The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an electron making a atomic electron transition, transition from a high energy state to a lower energy st ...

refers to the spectrum of radiation emitted by the compound due to electron transitions from a higher to a lower energy state. Light from many different sources contains various colors, each with its own brightness or intensity. A rainbow, or

, sends these component colors in different directions, making them individually visible at different angles. A graph of the intensity plotted against the frequency (showing the brightness of each color) is the frequency spectrum of the light. When all the visible frequencies are present equally, the perceived color of the light is white, and the spectrum is a flat line. Therefore, flat-line spectra in general are often referred to as ''white'', whether they represent light or another type of wave phenomenon (sound, for example, or vibration in a structure). In radio and telecommunications, the frequency spectrum can be shared among many different broadcasters. The

radio spectrum The radio spectrum is the part of the electromagnetic spectrum with frequencies from 0 Hz to 3,000 GHz (3 THz). Electromagnetic waves in this frequency range, called radio waves, are widely used in modern technology, particula ...

is the part of the

electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...

corresponding to frequencies lower below 300 GHz, which corresponds to wavelengths longer than about 1 mm. The

microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...

spectrum corresponds to frequencies between 300 MHz (0.3

GHz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one he ...

) and 300 GHz and wavelengths between one meter and one millimeter. Each broadcast radio and TV station transmits a wave on an assigned frequency range, called a ''channel''. When many broadcasters are present, the radio spectrum consists of the sum of all the individual channels, each carrying separate information, spread across a wide frequency spectrum. Any particular radio receiver will detect a single function of amplitude (voltage) vs. time. The radio then uses a

tuned circuit An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can ac ...

or tuner to select a single channel or frequency band and

demodulate Demodulation is extracting the original information-bearing signal from a carrier wave. A demodulator is an electronic circuit (or computer program in a software-defined radio) that is used to recover the information content from the modulated c ...

or decode the information from that broadcaster. If we made a graph of the strength of each channel vs. the frequency of the tuner, it would be the frequency spectrum of the antenna signal. In

astronomical spectroscopy Astronomical spectroscopy is the study of astronomy using the techniques of spectroscopy to measure the spectrum of electromagnetic radiation, including visible light, ultraviolet, X-ray, infrared and radio waves that radiate from stars and othe ...

, the strength, shape, and position of absorption and emission lines, as well as the overall

spectral energy distribution A spectral energy distribution (SED) is a plot of energy versus frequency or wavelength of light (not to be confused with a 'spectrum' of flux density vs frequency or wavelength). It is used in many branches of astronomy to characterize astron ...

of the continuum, reveal many properties of astronomical objects.

Stellar classification In astronomy, stellar classification is the classification of stars based on their stellar spectrum, spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a Prism (optics), prism or diffraction grati ...

is the categorisation of

star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...

s based on their characteristic electromagnetic spectra. The

spectral flux density In spectroscopy, spectral flux density is the quantity that describes the rate at which energy is transferred by electromagnetic radiation through a real or virtual surface, per unit surface area and per unit wavelength (or, equivalently, per unit ...

is used to represent the spectrum of a light-source, such as a star. In

radiometry Radiometry is a set of techniques for measurement, measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power (physics), power in space, as opposed to phot ...

and

colorimetry Colorimetry is "the science and technology used to quantify and describe physically the human color perception". It is similar to spectrophotometry, but is distinguished by its interest in reducing spectra to the physical correlates of color ...

(or

color science Color science is the scientific study of color including lighting and optics; measurement of light and color; the physiology, psychophysics, and modeling of color vision; and color reproduction. History Organizations * International Commiss ...

more generally), the

spectral power distribution In radiometry, photometry, and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination (radiant exitance). More generally, the term ''spectral power distribution'' ...

(SPD) of a

light source Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 terahe ...

is a measure of the power contributed by each frequency or color in a light source. The light spectrum is usually measured at points (often 31) along the

, in wavelength space instead of frequency space, which makes it not strictly a spectral density. Some

spectrophotometers Spectrophotometry is a branch of electromagnetic spectroscopy concerned with the quantitative measurement of the reflection or transmission properties of a material as a function of wavelength. Spectrophotometry uses photometers, known as spec ...

can measure increments as fine as one to two

nanometer 330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re ...

s. the values are used to calculate other specifications and then plotted to show the spectral attributes of the source. This can be helpful in analyzing the color characteristics of a particular source.

Mass spectrum

A plot of ion abundance as a function of

mass-to-charge ratio The mass-to-charge ratio (''m''/''Q'') is a physical quantity relating the ''mass'' (quantity of matter) and the ''electric charge'' of a given particle, expressed in units of kilograms per coulomb (kg/C). It is most widely used in the electrody ...

is called a mass spectrum. It can be produced by a

mass spectrometer Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a ''mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is used ...

instrument. The mass spectrum can be used to determine the quantity and

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...

of atoms and molecules.

Tandem mass spectrometry Tandem mass spectrometry, also known as MS/MS or MS2, is a technique in instrumental analysis where two or more mass analyzers are coupled together using an additional reaction step to increase their abilities to analyse chemical samples. A comm ...

is used to determine molecular structure.

Energy spectrum

In physics, the energy spectrum of a particle is the number of particles or intensity of a particle beam as a function of particle energy. Examples of techniques that produce an energy spectrum are

alpha-particle spectroscopy Alpha spectrometry (also known as alpha(-particle) spectroscopy) is the quantitative study of the energy of alpha particles emitted by a radioactive nuclide that is an alpha emitter. As emitted alpha particles are mono-energetic (i.e. not emitt ...

electron energy loss spectroscopy In electron energy loss spectroscopy (EELS) a material is exposed to a beam of electrons with a known, narrow range of kinetic energies. Some of the electrons will undergo inelastic scattering, which means that they lose energy and have their pa ...

, and

mass-analyzed ion-kinetic-energy spectrometry Mass-analyzed ion kinetic-energy spectrometry (MIKES) is a mass spectrometry technique by which mass spectra are obtained from a sector instrument that incorporates at least one magnetic sector plus one electric sector in reverse geometry (the b ...

Discrete spectrum

In physics, particularly in

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

, some

differential operator In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and return ...

s have discrete spectra, with gaps between values. Common cases include the

Hamiltonian Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian ...

and the

angular momentum operator In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum prob ...

Displacement

Oscillatory Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...

displacement Displacement may refer to: Physical sciences Mathematics and Physics *Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path ...

s, including

vibration Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic function, periodic, such as the motion of a pendulum ...

s, can also be characterized spectrally. * For

water wave In fluid dynamics, a wind wave, water wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result from the wind blowing over the water surface. The contact distance in the direction of t ...

s, see ''

wave spectrum In fluid dynamics, a wind wave, water wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result from the wind blowing over the water surface. The contact distance in the direction of t ...

'' and ''

tide spectrum The theory of tides is the application of continuum mechanics to interpret and predict the tidal deformations of planetary and satellite bodies and their atmospheres and oceans (especially Earth's oceans) under the gravitational loading of anot ...

''.

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 ...

and non-audible acoustic waves can also be characterized in terms of its spectral density, for example,

timbre In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or musical tone, tone. Timbre distinguishes different types of sound production, such as choir voice ...

and

musical acoustics Musical acoustics or music acoustics is a multidisciplinary field that combines knowledge from physics, psychophysics, organology (classification of the instruments), physiology, music theory, ethnomusicology, signal processing and instrument buil ...

Measurement

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 ...

, a

spectrogram A spectrogram is a visual representation of the spectrum of frequencies of a signal as it varies with time. When applied to an audio signal, spectrograms are sometimes called sonographs, voiceprints, or voicegrams. When the data are represen ...

is a visual representation of the frequency spectrum of sound as a function of time or another variable. A source of sound can have many different frequencies mixed. A

musical tone Traditionally in Western music, a musical tone is a steady periodic sound. A musical tone is characterized by its duration, pitch, intensity (or loudness), and timbre (or quality). The notes used in music can be more complex than musical ton ...

is characterized by its

harmonic spectrum A harmonic spectrum is a spectrum containing only frequency components whose frequencies are whole number multiples of the fundamental frequency; such frequencies are known as harmonics. "The individual partials are not heard separately but are ...

. Sound in our environment that we refer to as ''noise'' includes many different frequencies. When a sound signal contains a mixture of all audible frequencies, distributed equally over the audio spectrum, it is called

white noise In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, ...

. The

spectrum analyzer A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals. The input signal that most co ...

is an instrument which can be used to convert the

of the musical note into a visual display of the constituent frequencies. This visual display is referred to as an acoustic

. Software based audio spectrum analyzers are available at low cost, providing easy access not only to industry professionals, but also to academics, students and the

hobbyist A hobby is considered to be a regular activity that is done for enjoyment, typically during one's leisure time. Hobbies include collecting themed items and objects, engaging in creative and artistic pursuits, playing sports, or pursuing oth ...

. The acoustic spectrogram generated by the spectrum analyzer provides an

acoustic signature The term acoustic signature is used to describe a combination of acoustic emissions of sound emitters, such as those of ships and submarines. In addition, aircraft, machinery, and living animals can be described as having their own characteristic ...

of the musical note. In addition to revealing the fundamental frequency and its overtones, the spectrogram is also useful for analysis of the temporal attack,

decay Decay may refer to: Science and technology * Bit decay, in computing * Software decay, in computing * Distance decay, in geography * Decay time (fall time), in electronics Biology * Decomposition of organic matter * Tooth decay (dental caries ...

sustain In sound and music, an envelope describes how a sound changes over time. It may relate to elements such as amplitude (volume), frequencies (with the use of filters) or pitch. For example, a piano key, when struck and held, creates a near-immedi ...

, and

release Release may refer to: * Art release, the public distribution of an artistic production, such as a film, album, or song * Legal release, a legal instrument * News release, a communication directed at the news media * Release (ISUP), a code to ident ...

of the musical note.

References

{{reflist Concepts in physics Light