Later it expanded to apply to other waves, such as sound waves and sea 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", whose power spectrum 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 or mass-to-charge ratio in mass spectrometry. Spectrum is also used to refer to a graphical representation of the signal as a function of the dependent variable.
The prefix "spectro-" is used to form words relating to spectra. For example, a spectrometer is a device used to record spectra and spectroscopy is the use of a spectrometer for chemical analysis.
Electromagnetic spectrum refers to the full range of all frequencies of electromagnetic 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 called spectrograph or spectrometer. The visible spectrum is the part of the electromagnetic spectrum that can be seen by the human eye. The wavelength of visible light ranges from 390 to 700 nm.[4] The absorption spectrum of a chemical element or chemical 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. The emission spectrum 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 prism, 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 is the part of the electromagnetic spectrum corresponding to frequencies lower below 300 GHz, which corresponds to wavelengths longer than about 1 mm. The microwave 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 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 or tuner to select a single channel or frequency band and demodulate 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, the strength, shape, and position of absorption and emission lines, as well as the overall spectral energy distribution of the continuum, reveal many properties of astronomical objects. Stellar classification is the categorisation of stars based on their characteristic electromagnetic spectra. The spectral flux density is used to represent the spectrum of a light-source, such as a star.
In radiometry and colorimetry (or color science more generally), the spectral power distribution (SPD) of a light 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 the visible spectrum, in wavelength space instead of frequency space, which makes it not strictly a spectral density. Some spectrophotometers can measure increments as fine as one to two nanometers 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 of mass-to-charge ratio is called a mass spectrum. It can be produced by a mass spectrometer instrument.[8] The mass spectrum can be used to determine the quantity and mass of atoms and molecules. Tandem mass spectrometry is used to determine molecular structure.
In acoustics, a spectrogram 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's timbre is characterized by its harmonic spectrum. 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.[12]
The spectrum analyzer is an instrument which can be used to convert the sound wave of the musical note into a visual display of the constituent frequencies. This visual display is referred to as an acoustic spectrogram. 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. The acoustic spectrogram generated by the spectrum analyzer provides an acoustic signature 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, sustain, and release of the musical note.
Approximate frequency ranges corresponding to ultrasound, with rough guide of some applications
Acoustic spectrogram of the words "Oh, no!" said by a young girl, showing how the discrete spectrum of the sound (bright orange lines) changes with time (the horizontal axis)
The classical example of a continuous spectrum, from which the name is derived, is the part of the spectrum of the light emitted by excitedatoms of hydrogen that is due to free electrons becoming bound to a hydrogen ion and emitting photons, which are smoothly spread over a wide range of wavelengths, in contrast to the discrete lines due to electrons falling from some bound quantum 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. In quantum systems, continuous spectra (as in bremsstrahlung and thermal radiation) are usually associated with free particles, such as atoms in a gas, electrons in an electron beam, or conduction band electrons in a metal. In particular, the position and momentum 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 the phonons in a crystal.
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-linear filter; for example, when a pure tone is played through an overloaded amplifier,[17] or when an intense monochromaticlaser beam goes through a non-linear medium.[18] In the latter case, if two arbitrary sinusoidal signals with frequencies f and g are processed together, the output signal will generally have spectral lines at frequencies |mf + ng|, where m and n are any integers.
Discrete spectra are usually associated with systems that are bound in some sense (mathematically, confined to a compact space).[citation needed] The position and momentum operators have continuous spectra in an infinite domain, but a discrete (quantized) spectrum in a compact domain and the same properties of spectra hold for angular momentum, Hamiltonians and other operators of quantum systems.
The quantum harmonic oscillator and the hydrogen 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 the ionization.
The discrete part of the emission spectrum of hydrogen
Spectrum of sunlight above the atmosphere (yellow) and at sea level (red), revealing an absorption spectrum with a discrete part (such as the line due to O 2) and a continuous part (such as the bands labeled H 2O)
Spectrum of light emitted by a deuterium lamp, showing a discrete part (tall sharp peaks) and a continuous part (smoothly varying between the peaks). The smaller peaks and valleys may be due to measurement errors rather than discrete spectral lines.
^ OpenStax Astronomy, "Spectroscopy in Astronomy". OpenStax CNX. September 29, 2016 "OpenStax CNX". Archived from the original on February 17, 2017. Retrieved February 17, 2017.
^"Continuous Spectrum - klinics.lib.kmutt.ac.th". KMUTT: Thailands Science General. 2 (1): 22. Archived from the original(PDF) on 2022-08-20 – via KMUTT. 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.[dead link]
^Lindblom, Björn; Sundberg, Johan (2007). "The Human Voice in Speech and Singing". Springer Handbook of Acoustics. New York, NY: Springer New York. pp. 669–712. doi:10.1007/978-0-387-30425-0_16. ISBN978-0-387-30446-5.
^Popov, A. V.; Shuvalov, V. F.; Markovich, A. M. (1976). "The spectrum of the calling signals, phonotaxis, and the auditory system in the cricket Gryllus bimaculatus". Neuroscience and Behavioral Physiology. 7 (1). Springer Science and Business Media LLC: 56–62. doi:10.1007/bf01148749. ISSN0097-0549. PMID1028002. S2CID25407842.
![Classification of the spectrum of ocean waves according to wave period[9]](File:Munk_ICCE_1950_Fig1.svg)
![Spectrum of tides measured at Fort Pulaski in 2012.[10] This Fourier transform was computed using SourceForge[11]](File:Tides_Fourier_Transform.png)
