486 Wave MotionSection 16.6The Linear Wave EquationP16.43(a)A=+7 003 00 4 00...afyields A=40 0.(b)In order for two vectors to be equal, they must have the same magnitude and the samedirection in three-dimensional space. All of their components must be equal. Thus,7 0003 00.±±.±±±±ijkijk++=++ABCrequires ABC===7 0003 00.,,.and .(c)In order for two functions to be identically equal, they must be equal for every value ofevery variable. They must have the same graphs. InABCxDtExt+++=+++cos.cos...afaf07 003 004 002 00mm,the equality of average values requires that A=0. The equality of maximum valuesrequires B=7 00.mm. The equality for the wavelength or periodicity as a function of xrequires C=3 00.rad m. The equality of period requires D=4 00.rad s, and theequality of zero-crossings requires E=2 00.rad.*P16.44The linear wave equation is∂∂=∂∂222221yxvytIf yeb xvt=−afthen ∂∂= −−ytbveb xvtafand ∂∂=−yxbeb xvtaf∂∂=
This is the end of the preview.
access the rest of the document.