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484_Physics ProblemsTechnical Physics

484_Physics ProblemsTechnical Physics - 486 Wave Motion...

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486 Wave Motion Section 16.6 The Linear Wave Equation P16.43 (a) A = + 7 00 3 00 4 00 . . . a f yields A = 40 0 . (b) In order for two vectors to be equal, they must have the same magnitude and the same direction in three-dimensional space. All of their components must be equal. Thus, 7 00 0 3 00 . ± ± . ± ± ± ± i j k i j k + + = + + A B C requires A B C = = = 7 00 0 3 00 . , , . and . (c) In order for two functions to be identically equal, they must be equal for every value of every variable. They must have the same graphs. In A B Cx Dt E x t + + + = + + + cos . cos . . . a f a f 0 7 00 3 00 4 00 2 00 mm , the equality of average values requires that A = 0 . The equality of maximum values requires B = 7 00 . mm . The equality for the wavelength or periodicity as a function of x requires C = 3 00 . rad m . The equality of period requires D = 4 00 . rad s , and the equality of zero-crossings requires E = 2 00 . rad . *P16.44 The linear wave equation is = 2 2 2 2 2 1 y x v y t If y e b x vt = a f then = − y t bve b x vt a f and = y x be b x vt a f =
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