P18_027 - with points on a sphere of radius r in phase. If...

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27. (a) Let P be the power output of the source. This is the rate at which energy crosses the surface of any sphere centered at the source and is therefore equal to the product of the intensity I at the sphere surface and the area of the sphere. For a sphere of radius r , P =4 πr 2 I and I = P/ 4 πr 2 . The intensity is proportional to the square of the displacement amplitude s m .I fw ew r i t e I = Cs 2 m ,whe re C is a constant of proportionality, then Cs 2 m = P/ 4 πr 2 .T h u s s m = p P/ 4 πr 2 C =
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Unformatted text preview: with points on a sphere of radius r in phase. If is the angular frequency and k is the angular wave number then the time dependence is sin( kr t ). Letting b = p P/ 4 C , the displacement wave is then given by s ( r, t ) = r P 4 C 1 r sin( kr t ) = b r sin( kr t ) . (b) Since s and r both have dimensions of length and the trigonometric function is dimensionless, the dimensions of b must be length squared....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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