mPhys390-hw1-sol - January 17, 2007 Physics 390: Homework...

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Unformatted text preview: January 17, 2007 Physics 390: Homework set #1 Solutions Reading: Tipler & Llewellyn, Chapter 3 Questions: 1. Show that the classical wave equation 2 f t 2- c 2 2 f x 2 = 0 is satisfied by any function f that depends on x and t in the combination u = x ct : f ( x, t ) = f ( u ) = f ( x ct ). Solution: To see this, plug into the equation above: t f = f u u t = f u ( c ) 2 t 2 f = t parenleftbigg f t parenrightbigg = t bracketleftbigg f u ( c ) bracketrightbigg = ( c ) t f u = ( c ) u f u u t = ( c ) 2 f u 2 ( c ) = c 2 2 f u 2 similarly, 2 f x 2 = 2 f u 2 parenleftbigg u x parenrightbigg 2 = 2 f u 2 (1) = 2 f u 2 and, 2 f t 2- c 2 2 f x 2 = c 2 2 f u 2- c 2 2 f u 2 = 0 identically! 2. Plancks constant is h = 6 . 626 10 34 J s. What familiar physical quantity from classical me- chanics also has dimensions of J s? Solution: Angular momentum also has dimensions of J s. We will see that Plancks constant is closely related to quantization of angular momentum. 1 3. In what region of the electromagnetic spectrum does the blackbody radiation from a roomtem- perature object peak? What sorts of problems would we have if our eyes were sensitive in this region? Solution: Room temperature is about 290 K. Using the Wien displacement law, we have max = 2 . 898 10 3 m K 290 K = 1 10 5 m ....
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mPhys390-hw1-sol - January 17, 2007 Physics 390: Homework...

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