HW1_ExtraProblems

# HW1_ExtraProblems - Extra 3 You have a black body at...

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Homework 1 - Extra Problem January 2010 Extra 1 The wave equation in three dimensions is 2 ~ E ∂t 2 = c 2 2 ∂x 2 + 2 ∂y 2 + 2 ∂z 2 ~ E = c 2 2 ~ E (1) In class we gave the solution for the wave equation in a cavity with conducting walls at x = 0 , a ; y = 0 , a ; z = 0 , a as E x = E ox cos n x πx a sin n y πy a sin n z πz a cos(2 πνt ) (2) E y = E oy sin n x πx a cos n y πy a sin n z πz a cos(2 πνt ) (3) E z = E oz sin n x πx a sin n y πy a cos n z πz a cos(2 πνt ) . (4) (a) Show that the solution does indeed satisfy the wave equation, but that a particular condition needs to be maintained between the frequency ν and the integers n x , n y , n z . Extra 2 Consider a person to be a black body at a temperature of 37 C. How much power are we radiating (you will need to give a rough estimate for an adult surface area)? ( Optional : An adult male consumes 2 · 10 6 calories per day. Does energy balance indicate that we radiate power as black bodies? ) Extra 3

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Unformatted text preview: Extra 3 You have a black body at temperature T and can not remember Wien’s displacement law that relates T to the frequency of maximum emission ν max . You want to come up with a close alternative to ν max and decide to ﬁnd ν alternative through hν alt = kT. (5) Calculate by what factor is ν max smaller or larger than ν alt . If this factor is not so large (less than 10) then you found an easy way to approximate ν max . 1 Extra 4 - Optional Using the two expressions for the ﬂux of a black body, one as a function of frequency and the other as a function of wavelength, derive two expressions for the Wien displacement law. For a ﬁxed temperature T , does ν max λ max = c ? Give a reason for either answer. 2...
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