Webwhich is simply the expression CM-(25.28) for the celerity of linear waves. The first-order coefficient H 1is clearly a free parameter, and usually one defines H 1D› 1Dawhere ais the linear wave amplitude. Second order approximation For ND2we have hDH 1cosxCH 2cos2x; (20) and v xD› 1f 1.y/cosxC2› 2f 2.y/cos2x; (21) eSWvelocities v yD ... WebBecause the first order wave equation is linear, if a(x,t)andb(x,t)arebothsolutionsto (1.1) on an infinite domain, then any combination of c1a(x,t)+c2b(x,t)isalsoasolution. We will now exploit this to perform Fourier analysis on the first order wave equation. This analyis will be fairly simple but introduce concepts that will be used throughout.
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