chem3322_hwk1 - you consider all the possibilities Problem...

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Chem 3322 homework #1 – due Jan. 27, 2012 Problem 1 – linearity Assume that the function f ( x,t ) is a classical wave (namely, f ( x,t ) solves the one- dimensional classical wave equation) with speed v 1 . Assume, in addition, that the function g ( x,t ) is a classical wave with speed v 2 . Note 1: do not assume these functions are simple, one-color, waves; they may be more complicated. Note 2: the speeds v 1 and v 2 might not be equal to each other. Consider the function u ( x,t ) = af ( x,t ) + bg ( x,t ) where a and b are real numbers. Is the function u ( x,t ) a classical wave? Give a mathematical proof, and state any assumptions you make or conditions you need in order for the proof to work. Make sure
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Unformatted text preview: you consider all the possibilities. Problem 2 – total derivative In class we used the relationship ∇ V · dr = dV (1) where r = ( x,y,z ). a) Prove this relationship using mathematics. Hint: equation (H.11) on page 686 of your textbook is relevant. b) Explain part (a) at a conceptual level (no equations allowed). Hint: The 4 lines of text following equation (H.11) are relevant. Problem 3 – Classical Wave Equation Show that the function u ( x,t ) = e i ( kx-ωt ) solves the one-dimensional classical wave equa-tion. 1...
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This note was uploaded on 02/08/2012 for the course CHEM 3411 taught by Professor Nielsen during the Spring '06 term at University of Texas at Dallas, Richardson.

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