Mechanical resonance: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Gilliam
m Reverted edits by 80.254.147.188 (talk) to last version by Fountains of Bryn Mawr
Its not a misunderstanding
 
Line 1: Line 1:
{{Refimprove|date=February 2010}}
Hello, my name is Andrew and my wife doesn't like it at all. My working day occupation is an invoicing officer but I've currently applied for another one. What I love performing is soccer but I don't have the time recently. For a whilst I've been in Alaska but I will have to transfer in a yr or two.<br><br>My web blog: [http://brazil.amor-amore.com/irboothe free psychic readings]
 
'''Opacity''' is the measure of impenetrability to [[electromagnetic radiation|electromagnetic]] or other kinds of [[radiation]], especially visible [[light]].  In [[radiative transfer]], it describes the absorption and scattering of radiation in a [[transmission medium|medium]], such as a [[plasma (physics)|plasma]], [[dielectric]], [[radiation shield|shielding material]], glass, etc.  An '''opaque''' object is neither [[Transparency (optics)|transparent]] (allowing all light to pass through) nor [[translucent]] (allowing some light to pass through).  When light strikes an interface between two substances, in general some may be reflected, some absorbed, some scattered, and the rest transmitted (also see [[refraction]]). Reflection can be [[diffuse reflection|diffuse]], for example light reflecting off a white wall, or [[specular reflection|specular]], for example light reflecting off a mirror. An opaque substance transmits no light, and therefore reflects, scatters, or absorbs all of it. Both [[mirror]]s and [[carbon black]] are opaque.  Opacity depends on the [[frequency]] of the light being considered.  For instance, some kinds of [[glass]], while transparent in the [[visible light|visual range]], are largely opaque to [[ultraviolet]] light.  More extreme frequency-dependence is visible in the [[absorption line]]s of cold [[gas]]es. Opacity can be quantified in many ways; for example, see the article [[mathematical descriptions of opacity]].
 
For general information on what makes an object or medium opaque, see the articles on [[absorption (electromagnetic radiation)|absorption]], [[reflection (physics)|reflection]], and [[light scattering|scattering]]. These are the processes that lead to opacity.
 
==Quantitative definition==
{{See also|Extinction (astronomy)|attenuation coefficient}}
 
The words "opacity" and "opaque" are often used as colloquial terms for objects or media with the properties described above. However, there is also a specific, quantitative definition of "opacity", used in astronomy, plasma physics, and other fields, given here.
 
In this use, "opacity" is another term for the [[mass attenuation coefficient]] (or, depending on context, [[mass absorption coefficient]], the difference is described [[Absorption coefficient#Attenuation versus absorption|here]]) <math>\kappa_\nu</math> at a particular frequency <math>\nu</math> of electromagnetic radiation.
 
More specifically, if a beam of light with frequency <math>\nu</math> travels through a medium with opacity <math>\kappa_\nu</math> and mass density <math>\rho</math>, both constant, then the intensity will be reduced with distance ''x'' according to the formula
:<math>I(x) = I_0 e^{-\kappa_\nu \rho x}</math>
where
* ''x'' is the distance the light has traveled through the medium
* <math>I(x)</math> is the intensity of light remaining at distance ''x''
* <math>I_0</math> is the initial intensity of light, at <math>x = 0</math>
 
For a given medium at a given frequency,  the opacity has a numerical value that may range between 0 and infinity, with units of length<sup>2</sup>/mass.
 
===Planck and Rosseland opacity===
 
It is customary to define the average opacity, calculated using a certain weighting scheme. '''Planck opacity''' uses normalized [[Planck's law of black body radiation|Planck black body radiation energy density distribution]] as the weighting function, and averages <math>\kappa_\nu</math> directly. '''Rosseland opacity''' (after [[Svein Rosseland]]), on the other hand, uses a temperature derivative of [[Planck's law of black body radiation|Planck distribution]] (normalized) as the weighting function, and averages <math>\kappa_\nu^{-1}</math>,
:<math>\frac{1}{\kappa} = \frac{\int_0^{\infty} \kappa_{\nu}^{-1} u(\nu, T) d\nu }{\int_0^{\infty} u(\nu,T) d\nu}</math>.
The photon mean free path is  <math>\lambda_\nu = (\kappa_\nu \rho)^{-1}</math>. The Rosseland opacity is derived in the diffusion approximation to the radiative transport equation. It is valid whenever the radiation field is isotropic over distances comparable to or less than a radiation mean free path, such as in local thermal equilibrium.
In practice, the mean opacity for [[Thomson scattering|Thomson electron scattering]] is:
:<math>\kappa_{\rm es} = 0.20(1+X) {\rm\, cm}^2{\rm \,g}^{-1}</math>
where <math> X </math> is the hydrogen mass fraction.
For [[Bremsstrahlung|nonrelativistic thermal bremsstrahlung]], or free-free transitions, it is:
:<math>\kappa_{\rm ff}(\rho, T) = 0.64 \times 10^{23} (\rho[ {\rm g}~ {\rm\, cm}^{-3}])(T[{\rm K}])^{-7/2} {\rm\, cm}^2 {\rm\, g}^{-1}</math>.<ref>Stuart L. Shapiro and [[Saul Teukolsky|Saul A. Teukolsky]], "Black Holes, White Dwarfs, and Neutron Stars" 1983, ISBN 0-471-87317-9.</ref>
The Rosseland mean absorption coefficient including both scattering and absorption (also called the extinction coefficient) is:
:<math>\frac{1}{\kappa} = \frac{\int_0^{\infty} (\kappa_{\nu, {\rm es}} + \kappa_{\nu, {\rm ff}})^{-1} u(\nu, T) d\nu }{\int_0^{\infty} u(\nu,T) d\nu}</math>.<ref>George B. Rybicki and [[Alan Lightman|Alan P. Lightman]], "Radiative Processes in Astrophysics" 1979 ISBN 0-471-04815-1.</ref>
 
==See also==
* [[Absorption (electromagnetic radiation)]]
* [[Mathematical descriptions of opacity]]
* [[Molar absorptivity]]
* [[Reflection (physics)]]
* [[Scattering theory]]
* [[Transparency and translucency]]
 
==References==
{{reflist|1}}
 
[[Category:Optics]]
[[Category:Electromagnetic radiation]]
[[Category:Scattering, absorption and radiative transfer (optics)]]
[[Category:Spectroscopy]]
[[Category:Glass physics]]

Latest revision as of 19:44, 12 September 2014

Hello, my name is Andrew and my wife doesn't like it at all. My working day occupation is an invoicing officer but I've currently applied for another one. What I love performing is soccer but I don't have the time recently. For a whilst I've been in Alaska but I will have to transfer in a yr or two.

My web blog: free psychic readings