- For other uses, see Spectrum (disambiguation).
The noun spectrum (plural: spectra) has a variety of meanings. In most modern usages, there is a unifying theme of a variety of possible cases between extremes at either end. Older usages were not necessarily on that same unifying theme, but nonetheless led to the modern ones through a sequence of events set out below. Some modern usages in mathematics evolved out of that unifying theme but may be difficult to recognize as fitting into it.
Ghosts
Originally a spectrum was what is now called a spectre, i.e., a phantom or apparition. Spectral evidence is testimony about what was done by spectres of persons not present physically, or hearsay evidence about what ghosts or apparitions of Satan said. It was used to convict a number of persons of witchcraft at Salem, Massachusetts in the late 17th century.
Modern (17th through 21st centuries) meaning in the physical sciences
High-resolution spectrum of the Sun showing thousands of elemental absorption lines ( fraunhofer lines). In the 17th century the word spectrum was introduced into optics, referring to the range of colors observed when white light was dispersed through a prism. Soon the term referred to a plot of light intensity as a function of frequency or wavelength. Max Planck later realized that frequency represents electromagnetic energy:
- <math> E = h \nu <math>
where E is the energy of a photon, h is Planck's constant, and <math> \nu <math> is the frequency of the light.
The word spectrum then took on the obvious analogous meaning in reference to other sorts of waves, such as sound wave, or other sorts of decomposition into frequency components. Thus a spectrum is a usually 2-dimensional plot, of a compound signal, depicting the components by another measure. Sometimes, the word spectrum refers to the compound signal itself, such as the "spectrum of visible light", a reference to those electromagnetic waves which are visible to the human eye.
Physical acoustics of music
- See timbre. Spectrum is one of the determinants of the timbre or quality of a sound. It is the relative strength of pitches called harmonics and partials (collectively overtones) at various frequencies usually above the fundamental frequency, which is the actual note named (eg. an A).
Meanings of spectrum in mathematics
The various meanings of the word spectrum in mathematics are derived (some fairly directly; some less so) from the meanings in the physical sciences.
Other disciplines
The meanings of spectrum in some other disciplines, including pharmacology, politics, and psychology evolved by analogy with the meanings in the physical sciences: just as dispersed colored light ranged from one end of the rainbow to the other, so also other things that range from one extreme to another were called spectra.
- The spectrum of activity of an antibiotic evaluates how wide a range of infections can be treated.
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