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Hello.. i need help with two homework questions if anyone would be so kind. I do not know where to begin on solving these questions. The questions are as follows: 1. If the angular frequencies of waves in a three-dimensional box of sides L generalize to: Ω = πc/L (n x ²+ n y ²+ n z ²)^1/2 Where all n are integers, show that the number of distinct states in the frequency interval f to f + Δ f ( f= Ω/2 π) is given by (where f is large) dN = 4 π(L ^3/c^3) f ²d f 2. Let the energy density in the frequency interval f to f + df within a blackbody at temperature T be dU( f ,T). Show that the power emitted through a small hole of area ΔA in the container is c/4dU ( f ,T) ΔA THANK YOU!


Hello.. i need help with two homework questions if anyone would be so kind.

I do not know where to begin on solving these questions.

The questions are as follows:



1. If the angular frequencies of waves in a three-dimensional box of sides L generalize to:



Ω = πc/L (nx²+ny²+nz²)^1/2



Where all n are integers, show that the number of distinct states in the frequency interval f to f + Δf
(f=Ω/2π) is given by (where f is large)



dN = 4
π(L^3/c^3)f²df



2. Let the energy density in the frequency interval f to f + df within a blackbody at temperature T be dU(f,T). Show that the power emitted through a small hole of area
ΔA in the container is



c/4dU
(f,T)ΔA





THANK YOU!

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Grade:upto college level

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