phy392_supplementary_coursenotes_2011

phy392_supplementary_coursenotes_2011 - PHY 392S PHYSICS OF...

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PHY 392S PHYSICS OF CLIMATE SUPPLEMENTARY COURSE NOTES Spring Term, 2011 Prof. Kimberly Strong Department of Physics University of Toronto Based on PHY315 notes of Prof. James R. Drummond
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PHY 315S - Radiation In Planetary Atmospheres -1- A ( x , t ) ± A ( x , t ² 1/ f ) A ( x , t ) ± A ( x ² ± , t ) PHY 315S Radiation In Planetary Atmospheres Introduction Since this entire course is going to deal with radiation we should consider initially what we mean by radiation and what we already know about it. The first few lectures therefore will be in the nature of revision/levelling in which we shall revise some of the basic properties of radiation. Radiation as Wave Motion By this time you will all be aware that when we talk of radiation in an atmospheric context we do not normally mean nuclear or particle radiation but electromagnetic radiation as defined by solutions of Maxwell's equations. These electromagnetic wave phenomena have been studied fairly extensively over many centuries as the wave theory of light and associated frequencies. Briefly light is considered to be a wave-like phenomenon with a propagation velocity of 2.998 x 10 8 ms -1 in a vacuum and a velocity μ times slower in a medium, where μ is the refractive index of the medium and is (almost) invariably greater than unity. Light therefore travels fastest in vacuum and slower in a material medium. A wave motion has a frequency and wavelength associated with it such that the frequency is the time taken for the disturbance to execute one complete cycle at a point in space and the wavelength is the distance along the direction of propagation for one complete cycle of the motion at a particular time instant. We can express this as: and where the direction of propagation is assumed to be in the x direction. We can therefore combine these two relationships with the velocity of propagation, c , to give the relationship
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PHY 315S - Radiation In Planetary Atmospheres -2- ± ± c f A ( x , t ) ± a sin 2 % x ± ² 2 % ft There are several other simple relationships which we routinely use in considering these waveforms. Firstly, by associating a single frequency f with the wave we have presupposed that it has a sinusoidal form such that: where the minus sign comes from a consideration of the direction of propagation (from x = 0 to x = ± ). In order to avoid carrying factors of 2 % around with us we therefore define the wave vector k as k = 2 % / ± and the angular frequency 7 = 2 % f . In atmospheric situations we also run into the quantity 1/ ± often enough to merit a special symbol and I denote that as ² ± = 1/ ± . To complete a survey of the notation we also should remember that the symbol ² is also used for frequency. A problem should be noted here concerning the symbols ² and ² ± which I use for frequency and "wavenumber" respectively. Some authors reverse the definitions - sorry but it's too late now to correct that situation and you will just have to be careful which is which.
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This note was uploaded on 02/19/2011 for the course PHYSICS 392 taught by Professor Weak during the Spring '11 term at Toledo.

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phy392_supplementary_coursenotes_2011 - PHY 392S PHYSICS OF...

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