What is Spectrum: Definition and 764 Discussions

A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary, without steps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism. As scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum. It thereby became a mapping of a range of magnitudes (wavelengths) to a range of qualities, which are the perceived "colors of the rainbow" and other properties which correspond to wavelengths that lie outside of the visible light spectrum.
Spectrum has since been applied by analogy to topics outside optics. Thus, one might talk about the "spectrum of political opinion", or the "spectrum of activity" of a drug, or the "autism spectrum". In these uses, values within a spectrum may not be associated with precisely quantifiable numbers or definitions. Such uses imply a broad range of conditions or behaviors grouped together and studied under a single title for ease of discussion. Nonscientific uses of the term spectrum are sometimes misleading. For instance, a single left–right spectrum of political opinion does not capture the full range of people's political beliefs. Political scientists use a variety of biaxial and multiaxial systems to more accurately characterize political opinion.
In most modern usages of spectrum there is a unifying theme between the extremes at either end. This was not always true in older usage.

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  1. G

    The Maxwell equation and the Fourier Spectrum of an Electric Field

    Hi. I have an electric field E(r) which can be equivalently characterized by its Fourier spectrum \tilde{E}(k) through E(r)\propto\int\tilde{E}(k)exp[ik\cdotr]dk The Maxwell equation states that in a homogeneous and isotropic medium ∇\cdotE=0 So, applying this equation to my Fourier...
  2. S

    Band spectrum and line spectrum

    why do the atoms in excited state alone could emit line spectra?can't they emit when they are not in gaseous state? why only molecules can emit band spectra?can't atoms emit them
  3. M

    Highest order of spectrum given two wavelengths

    Homework Statement I've attached the problem Homework Equations d*sinθ=mλ The Attempt at a Solution I've tried a couple of methods. I considered solving for m when θ=90 degrees => sinθ=1 because 90 degrees is the highest possible angle and will (in my mind at least) yield the highest order...
  4. E

    Sun Emission Spectrum: Redshift/Blueshift & Visible Light

    Is the rather continuous spectrum of the Sun due to redshift/blueshift of the radiation emenating from the Sun? I understand that the emission spectrum of Hydrogen in the visible range is quantized to four discrete values, but I'm trying to understand how all frequencies of visible light are...
  5. T

    Do less bright stars have redder spectrum?

    Do less bright stars have redder spectrum?
  6. H

    What do the peaks in the reflectance spectrum of silicon samples represent?

    Hello, I am currently analysing some relfectance data I obtained from measurements on several silicon samples. During the process I used the standard fresnel coefficients, and suddenly I began to wonder, what the peaks describe? The last graph at this link shows it for normal incident light...
  7. M

    Understanding the Linear Power Spectrum: How Do BAOs Create Wiggles?

    Dear Experts, I try to understand power spectra for large scale structure and CMB analyses for my exams. I constantly find the expression for linear power spectra P(k) = A\cdot k^{n_s}\cdot T^2(k). I understand that this comes from primodial primodial fluctuations and the tranfer function...
  8. V

    Determining index of refraction and wavelength of a visible spectrum?

    Homework Statement You decide to become a forensic pathologist because you enjoy working with dead people-they don't talk back-more than with the living. In one murder investigation, you find an unknown liquid in the victim's stomach. To identify this liquid, you pour a known amount of it onto...
  9. P

    Emission spectrum wavelengths.

    Something that bugged me when doing this lab. Standard little glass vials of gas, toss it in a 5kV potential make pretty color, look through diffraction grating see the individual wavelengths that are the finger prints of the element. My question however are all wavelengths equally...
  10. S

    Why Does the Continuous Emission Spectrum Depend Only on Temperature?

    why does the continuous emission spectrum depends only on the temperature of the solution and not on the characteristics of the source?i could not understand this.someone please explain me this:uhh:
  11. D

    Trace of operator with continuous spectrum

    Greetings, I must be missing something obvious but how is Tr{} defined exactly in case of contunuous spectrum operators? Everywhere I look I see it defined as a sum of [possibly infinite sequence of] eigenvalues. Is the following correct: Given Q = \int f(q) \left| q\right\rangle...
  12. S

    Energy spectrum of electromagnetic showers.

    Homework Statement Use the simple model for electromagnetic showers (explained below) to show that the energy spectrum of all secondary particles contained in an electromagnetic shower falls like E^{-2} for E_0 >> E >> E_c The Attempt at a Solution An electron or a photon with energy E_0...
  13. S

    Can LED's emit monochromatic light as efficiently as broad spectrum?

    I read that many high pressure sodium and high pressure mercury street lights are being replaced with much more efficient LED lights, which fortunately point downwards instead of sending light sideways at star gazers like me, or into the sky where it refracts back down and hazes over the stars...
  14. Philosophaie

    Spectrum of Light from Hydrogen

    The visible spectrum of light from hydrogen displays four wavelengths, 410 nm, 434 nm, 486 nm, and 656 nm normally. Which changes when a telescope is pointed at a Galaxy that is moving away?
  15. ajayguhan

    Understanding Spectrum: Types and Interactions with Matter

    What is spectrum? Today my teacher started the class by saying we are going to see about spectroscopy which deals with interaction of electromagnetic radiation with matter and there are two types of spectrum the atomic spectrum and the molecular spectrum. He didn't even say us what is...
  16. K

    Spectrum of Momentum operator in the Hilbert Space L^2([-L,L])

    Homework Statement Find the spectrum of the Momentum operator in the Hilbert Space defined by L^2([-L,L]), consisting of all square integrable functions ψ(x) in the range -L, to L Homework Equations We can get the resolvent set containting all λ in ℂ such that you can always find a...
  17. F

    Sketching the Spectrum of the Signal x(t)

    Homework Statement Make a sketch of the spectrum of the signal defined by: x(t) = \sum_{k = -3}^{3}\frac{1}{1+j\pi k}e^{j4\pi kt} Use polar notation for the phasors on the plot, and sketch the frequency axis in Hz. Homework Equations The Attempt at a Solution a_{k} =...
  18. M

    Doubt in electromagnetic spectrum

    In electromagnetic spectrum, why there is no radiation less than wavelength of Gamma rays and waves higher than the wavelength of Radio waves?
  19. M

    Unusual SNR in the guide of a Spectrum Analyzer

    If I posted in the wrong section, please feel free to move the thread in the correct one. Since this is my first post in the forum, I have yet to get a good grasp of it. With that said, let's begin! Prologue: SNR (Signal to Noise Ratio), sometimes indicated with S/N, is a very important...
  20. C

    Difference in energy between visible line spectrum and ultraviolet?

    Homework Statement The emission spectrum of an unknown element contains two lines - one in the visible portion of the spectrum, and the other, ultraviolet. Based on the following figure and what you know about Niels Bohr's model of the atom, account for the difference in energy between these...
  21. M

    Wave numbers of Power Spectrum

    Hi. I read some basic cosmology where it is always said that density fluctuations, pertubations can be described in modes of waves. In particular if you use linearised theory where δ(x,t) is Fourier transformed δ(k,t). What exactly is the reason for this? What do the wave modes describe...
  22. D

    Is an emission spectrum really independent of excitation wavelength?

    I've often read that the emission spectrum of a fluorescent molecule is independent of the wavelength used for the excitation. But what happens in the case of a small Stoke's shift where the excitation and emission wavelengths overlap? If I use a narrow band excitation with a wavelength in...
  23. P

    Trouble Collecting IR Spectrum of a-Si:H

    I am working on my thesis for my masters in physics, and am running into some issues while trying to gather an IR spectrum of my hydrogenated amorphous silicon (a-Si:H). I am depositing my films using PECVD onto a glass microscope slide substrate. The films I have used so far have been 0.2-0.4...
  24. K

    Relative Size Of Electro-Magnetic Spectrum

    I Watched A Video . In Which , It's Mentioned That The Relative Size Of.. Gamma Rays - Atomic Nucleus X-Rays - Atom Ultra-Violet Rays - DNA Visible Light - Bacteria ... Radio Waves - Mountain Ranges What's Mean By Relative Size ? I'm Confused Alot ! Thanks Alot In Advance For...
  25. V

    Exploring the Interactions between Electromagnetic Spectrum and Living Organisms

    Hi, I would like to do more studies and research in electromagnetic spectrum. And I am interested very much in these waves and it's interaction with human or living things or matter. So please provide me with the information about what kind of courses I should take. I will complete my post...
  26. H

    Why is there a small variation in the spectrum of the same element?

    why doesn't the uncertainty principle lead to small discrepancies in the spectrum of the same element in different situations? I think that since there is a whole area for the electron to jump from and to and therefore a small range of values of possible jumps for a single shell, so there...
  27. P

    What is the frequency spectrum for a single photon?

    According to the Einstein light-quantum hypothsis, the photon energy is given by E = hbar*ω. If taking the photon as a very short light pulse, then the frequency spectrum is extremely wide in terms of Fourier-transform theory. How to understand the frequency ω in E = hbar*ω if taking the...
  28. S

    Graphing Fourier Spectra of AM Signals with Sin^3 Carrier

    Homework Statement I am trying to figure out how to graph the signal spectra of an AM signal where the message m(t) is multiplied by the carrier, which is sin^3 (wt) instead of cos (wt). I can do the FT but I do not know how to graph this since there are imaginary numbers as coefficients...
  29. D

    Relation between spectra of operator and spectrum of a fourier transfo

    Hello, Something I have some time wondering and still couldn't find the answer is to this question: if there is some relation between the Spectrum (functional analysis) and the Frequency spectrum in Fourier Analysis. Now that I think about it there seems to be a casuality the use of the...
  30. D

    Useful Representations of Log Audio Frequency Spectrum

    Hi everyone, So I'm trying to basically generate a list of numbers between 20 and 20,000 (Hz) in log space that will give good resolution to parts of the audio spectrum that matter! After all that is the point of using log scale for frequency in the first place. The list generator I have...
  31. B

    How to absorb a characteristic line in the spectrum

    I have an x-ray tube. When I see the spectrum, I notice the characteristic lines of the anode. What do I have to do if I want to absorb a characteristic line? I have thought that I can add a filter. But.. which filter? Should it be an element such that the bound energy for the K-shell electrons...
  32. R

    Find the spectrum of the 2nd excited states.

    Homework Statement A state at the 2nd exited level is of the form: ##|\epsilon>=(\epsilon_{\mu\nu}\alpha^\mu_{-1}\alpha^\nu_{-1}+\epsilon_{\mu}\alpha^\nu_{-2})|0;p>## Find the spectrum of the 2nd excited states, the value of the mass squared, the condition for the state to be physical, and the...
  33. U

    Orbit about star, emission spectrum of light

    Homework Statement Show that in the Bohr model, the frequency of revolution of an electron in its nth In classical physics, the frequency of revolution of the electron is equal to the frequency of radiation it emits. Show that when n is very large, the frequency of revolution is equal...
  34. U

    How Is the Rydberg Constant Calculated from Photon Absorption Wavelengths?

    Homework Statement The following photon wavelengths are observed in absorption at room temperature from an ionized atomic gas with a single electron orbiting the nucleus: λ= 13:5 nm, 11:4 nm, 10:8 nm. Use this data to determine the effective Rydberg constant and the nuclear charge...
  35. U

    Spectrum of the Hamiltonian in QFT

    I know in ordinary QM, the spectrum of the Hamiltonian \{ E_{n}\} gives you just about everything you need for the system in question (roughly speaking). So what happens to this spectrum in QFT where |\psi\rangle is now a multiparticle wavefunction in some Fock space? I've been trying to...
  36. A

    Spectrum of a linear operator on a Banach space

    I'm trying to understand the spectrum and resolvent of a linear operator on a Banach space in as much generality as I possibly can. It seems that the furthest the concept can be "pulled back" is to a linear operator T: D(T) \to X, where X is a Banach space and D(T)\subseteq X. But here are a...
  37. J

    Understanding the spectrum of frequencies

    What is the distinction between EM waves and Sound waves. I know that sound is cyclical vibrations in some sort of medium. When the frequency increases, do these vibrations become EM waves? I know that EM waves do not need a physical medium. But they are still energy, and sound is energy. So...
  38. J

    Linear vs non linear matter power spectrum

    Hi, I have troubles understanding the difference between linear and non linear matter power spectrum. These words are commonly used in the litterature, but I have found no definitions yet. My understanding is that there is one definition of the power spectrum for matter distribution...
  39. M

    Atomic Spectra: Study of Symmetrical Lines from n=1

    When doing an experiment in order to observe the atomic spectra of some gas. We observe while peaking through the diffraction grating, symmetrical lines starting from n=1. Where does this symmetry arise from? Why do we see the same spectrum repeated on both, left side and right side. As if...
  40. R

    How can I obtain the gamma spectrum of an Am-Be source in MCNPX 2.6?

    Hi I want to define an Am-Be source in MCNPX 2.6 I have Neutron spectrum But I don't have Gamma spectrum of this source. Please Help!
  41. P

    Electron Spectrum in Beta Decay

    Homework Statement A nucleus N1 decays through beta decay to nucleus N2. The mass difference between N1 and N2 is ΔM. The differential decay rate may be written as: dw=p(E_e)dE_e p(E_e) \propto E_e (E_e^2-(m_ec^2))^{1/2}(\Delta Mc^2-E_e)((\Delta Mc^2-E_e)^2-(m_vc^2)^2)^{1/2} where Ee is the...
  42. M

    Signal spreading in spread spectrum technology (DSSS)

    Hi, I've been trying to understand DSSS, but I'm not an engineer and have trouble with one point. I get the fact that multiplying the user signal with the chip sequence is what spreads the signal. My question is, why is this? If the data rate is, say, 1 bps, and the chip sequence 1000 bits...
  43. P

    Why is Far-UV spectrum unobservable

    Hi couldn't find a similar thread so thought i'd make one. I keep seeing around the web that the far-UV spectrum is unobservable (context is looking at the spectra of AGN) but no-one seems to explain why. I think that its something to do with hydrogen strongly absorbs at these wavelengths...
  44. J

    Discrete time spectrum, finding possible continuous-time signals.

    The discrete-time spectrum of a sampled continuous-time signal x(t) is shown in the figure above, where (A = 9.8exp(-j0.06π), B = 0.51π, C = -0.27π, and D = 1.9exp(-j0.41π) ). If the sampling frequency is 4928, which of the following continous-time signals is a possible solution for x(t)...
  45. H

    Using a spectrum analyzer to find LC resonance?

    Hi everyone, I am using a signal generator in series with a RLC circuit, generating an AC signal at 1kHz. I have my probes connected across the resistor When I change the timescale the Fres bandwidth changes on the spectrum analyzer. At 1mS the resonant bandwidth is from 25kHz-50kHz At...
  46. X

    Archived Atomic Spectrum of an Unknown Element

    Homework Statement When an electron drops from the M shell (n = 3) to a vacancy in the K shell (n = 1), the measured wavelength of the emitted x-ray is found to be 0.0897 nm. Identify the element. Homework Equations E = 1240 / λ E = (-13.6 / n^2) * (Zeff^2) The Attempt at a...
  47. jk22

    Polarization modulation spectrum

    hello all. If one uses polarization modulation of radio waves does this imply a broad frequency spectrum knowing the carrier frequency and amplitude remain the same only the direction of the electric field is being changed ?
  48. S

    Negative frequencies in spectrum analysis

    Negative frequencies in spectrum analysis... Hello everyone... When we do the frequency analysis of a signal using Fourier transform, we get spectrum at negative frequencies also. What are they and what is the physical significance of such frequencies? Its hard for me to imagine a negative...
  49. J

    Why are our eyes tuned to a specific band of the EM spectrum?

    I mean why is it that the eye evolved to detect "visible" light instead of, say, microwaves. What is it about the visible light spectrum?
  50. J

    Zero point energy in thermal noise spectrum?

    This is a question about the proper form for thermal noise from a resistor. This is purely academic for me - I always work in the regime where \hbar \omega << k T so the noise spectrum is simply P \approx kT. When this no longer holds, quantum effects matter of course. Then I have seen...
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