In thephysical sciences, the termspectrum was introduced first intooptics byIsaac Newton in the 17th century, referring to the range of colors observed when white light wasdispersed through aprism.[1][2] Soon the term referred to a plot of lightintensity orpower as a function offrequency orwavelength, also known as aspectral density plot.
Later it expanded to apply to otherwaves, such assound waves andsea waves that could also be measured as a function of frequency (e.g.,noise spectrum,sea wave spectrum). It has also been expanded to more abstract "signals", whosepower spectrum can beanalyzed andprocessed. The term now applies to any signal that can be measured or decomposed along a continuous variable, such as energy inelectron spectroscopy or mass-to-charge ratio inmass spectrometry. Spectrum is also used to refer to a graphical representation of the signal as a function of the dependent variable.
InLatin,spectrum means "image" or "apparition", including the meaning "spectre".Spectral evidence is testimony about what was done by spectres of persons not present physically, orhearsay evidence about what ghosts or apparitions ofSatan said. It was used to convict a number of persons ofwitchcraft atSalem, Massachusetts in the late 17th century. The word "spectrum" [Spektrum] was strictly used to designate a ghostly opticalafterimage byGoethe in hisTheory of Colors andSchopenhauer inOn Vision and Colors.
The prefix "spectro-" is used to form words relating to spectra. For example, aspectrometer is a device used to record spectra andspectroscopy is the use of a spectrometer forchemical analysis.
Electromagnetic spectrum refers to the full range of all frequencies ofelectromagnetic radiation[3] and also to the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object. Devices used to measure an electromagnetic spectrum are calledspectrograph orspectrometer. Thevisible spectrum is the part of the electromagnetic spectrum that can be seen by thehuman eye. The wavelength of visible light ranges from390 to 700 nm.[4] Theabsorption spectrum of achemical element orchemical compound 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. Theemission spectrum refers to the spectrum of radiation emitted by the compound due toelectron 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, orprism, 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 aswhite, 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. Theradio spectrum is the part of theelectromagnetic spectrum corresponding to frequencies lower below 300 GHz, which corresponds to wavelengths longer than about 1 mm. Themicrowave spectrum corresponds to frequencies between 300 MHz (0.3 GHz) and 300 GHz and wavelengths between one meter and one millimeter.[5][6] Each broadcast radio and TV station transmits a wave on an assigned frequency range, called achannel. 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 atuned circuit or tuner to select a single channel or frequency band anddemodulate 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.
Inastronomical spectroscopy, the strength, shape, and position of absorption and emission lines, as well as the overallspectral energy distribution of the continuum, reveal many properties of astronomical objects.Stellar classification is the categorisation ofstars based on their characteristic electromagnetic spectra. Thespectral flux density is used to represent the spectrum of a light-source, such as a star.
Inradiometry andcolorimetry (orcolor science more generally), thespectral power distribution (SPD) of alight source 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 thevisible spectrum, in wavelength space instead of frequency space, which makes it not strictly a spectral density. Somespectrophotometers can measure increments as fine as one to twonanometers and even higher resolution devices with resolutions less than 0.5 nm have been reported.[7] 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.
A plot of ion abundance as a function ofmass-to-charge ratio is called a mass spectrum. It can be produced by amass spectrometer instrument.[8] The mass spectrum can be used to determine the quantity andmass of atoms and molecules.Tandem mass spectrometry is used to determine molecular structure.
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 arealpha-particle spectroscopy,electron energy loss spectroscopy, andmass-analyzed ion-kinetic-energy spectrometry.
Oscillatorydisplacements, includingvibrations, can also be characterized spectrally.
![Classification of the spectrum of ocean waves according to wave period[9]](/mt/?noimg=&dark=on&url=http%3a%2f%2fen.wikipedia.org%2fwiki%2fFile%3aMunk_ICCE_1950_Fig1.svg)
![Spectrum of tides measured at Fort Pulaski in 2012.[10] This Fourier transform was computed using SourceForge[11]](/mt/?noimg=&dark=on&url=http%3a%2f%2fen.wikipedia.org%2fwiki%2fFile%3aTides_Fourier_Transform.png)
Inacoustics, aspectrogram 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. Amusical tone'stimbre is characterized by itsharmonic spectrum. Sound in our environment that we refer to asnoise includes many different frequencies. When a sound signal contains a mixture of all audible frequencies, distributed equally over the audio spectrum, it is calledwhite noise.[12]
Thespectrum analyzer is an instrument which can be used to convert thesound wave of the musical note into a visual display of the constituent frequencies. This visual display is referred to as an acousticspectrogram. Software based audio spectrum analyzers are available at low cost, providing easy access not only to industry professionals, but also to academics, students and thehobbyist. The acoustic spectrogram generated by the spectrum analyzer provides anacoustic signature of the musical note. In addition to revealing the fundamental frequency and its overtones, the spectrogram is also useful for analysis of the temporalattack,decay,sustain, andrelease of the musical note.
In thephysical sciences, the spectrum of aphysical quantity (such asenergy) may be calledcontinuous if it is non-zero over the whole spectrum domain (such asfrequency orwavelength) ordiscrete if it attains non-zero values only in adiscrete set over theindependent variable, withband gaps between pairs ofspectral bands orspectral lines.[13]
The classical example of a continuous spectrum, from which the name is derived, is the part of thespectrum of the light emitted byexcitedatoms ofhydrogen that is due to freeelectrons becoming bound to a hydrogen ion and emitting photons, which are smoothly spread over a wide range of wavelengths, in contrast to thediscrete lines due to electrons falling from some boundquantum state to a state of lower energy. As in that classical example, the term is most often used when the range of values of a physical quantity may have both a continuous and a discrete part, whether at the same time or in different situations. Inquantum systems, continuous spectra (as inbremsstrahlung andthermal radiation) are usually associated with free particles, such as atoms in a gas, electrons in anelectron beam, orconduction band electrons in ametal. In particular, theposition andmomentum of a free particle has a continuous spectrum, but when the particle is confined to a limited space its spectrum becomes discrete.
Often a continuous spectrum may be just a convenient model for a discrete spectrum whose values are too close to be distinguished, as in thephonons in acrystal.
The continuous and discrete spectra of physical systems can be modeled infunctional analysis as different parts in thedecomposition of the spectrum of alinear operator acting on afunction space, such as theHamiltonian operator.
The classical example of a discrete spectrum (for which the term was first used) is the characteristic set of discretespectral lines seen in theemission spectrum andabsorption spectrum of isolatedatoms of achemical element, which only absorb and emit light at particularwavelengths. The technique ofspectroscopy is based on this phenomenon.
Discrete spectra are seen in many other phenomena, such as vibratingstrings,microwaves in ametal cavity,sound waves in apulsating star, andresonances in high-energyparticle physics. The general phenomenon of discrete spectra in physical systems can be mathematically modeled with tools offunctional analysis, specifically by thedecomposition of the spectrum of alinear operator acting on afunctional space.
Inclassical mechanics, discrete spectra are often associated towaves andoscillations in a bounded object or domain. Mathematically they can be identified with theeigenvalues ofdifferential operators that describe the evolution of some continuous variable (such asstrain orpressure) as a function of time and/or space.
Discrete spectra are also produced by somenon-linear oscillators where the relevant quantity has a non-sinusoidalwaveform. Notable examples are the sound produced by thevocal cords of mammals.[14][15]: p.684 and thestridulation organs ofcrickets,[16] whose spectrum shows a series of strong lines at frequencies that are integer multiples (harmonics) of theoscillation frequency.
A related phenomenon is the appearance of strong harmonics when a sinusoidal signal (which has the ultimate "discrete spectrum", consisting of a single spectral line) is modified by a non-linearfilter; for example, when apure tone is played through an overloadedamplifier,[17] or when an intensemonochromaticlaser beam goes through anon-linear medium.[18] In the latter case, if two arbitrary sinusoidal signals with frequenciesf andg are processed together, the output signal will generally have spectral lines at frequencies |mf +ng|, wherem andn are any integers.
Inquantum mechanics, the discrete spectrum of anobservable refers to thepure point spectrum ofeigenvalues of theoperator used to model that observable.[19][20]
Discrete spectra are usually associated with systems that arebound in some sense (mathematically, confined to acompact space).[citation needed] Theposition andmomentum operators have continuous spectra in an infinite domain, but a discrete (quantized) spectrum in a compact domain and the same properties of spectra hold forangular momentum,Hamiltonians and other operators of quantum systems.
Thequantum harmonic oscillator and thehydrogen atom are examples of physical systems in which the Hamiltonian has a discrete spectrum. In the case of the hydrogen atom the spectrum has both a continuous and a discrete part, the continuous part representing theionization.
OpenStax Astronomy, "Spectroscopy in Astronomy". OpenStax CNX. September 29, 2016"OpenStax CNX".Archived from the original on February 17, 2017. RetrievedFebruary 17, 2017.In physics, a continuous spectrum usually means a set of achievable values for some physical quantity (such as energy or wavelength), best described as an interval of real numbers. It is the opposite of a discrete spectrum, a set of achievable values that are discrete in the mathematical sense where there is a positive gap between each value.
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