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Question about the wave equation 
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#1
Dec1212, 11:47 AM

P: 208

Hello,
is it possible for one to assume a straightline propagation of an e.m. wave and constant velocity c? If so, is it possible to simplify the wave equation u_{tt}=c^{2}u_{xx} by expressing the spatial variable x through the time variable t? x must be a function of t, since the motion is rectilinear with constant c. Then, x = x(t) and x is no longer independent variable. Then the above PDE should be rewritten in terms of t only, since u(x,t)=u(x(t),t)=u(t) Does this make sense? 


#2
Dec1312, 06:37 AM

P: 752

http://en.wikipedia.org/wiki/Wave_equation http://people.ccmr.cornell.edu/~much...es/node18.html http://hyperphysics.phyastr.gsu.edu...ves/waveq.html 


#3
Dec1312, 03:17 PM

PF Gold
P: 1,150

If you have some function x1(t), you can define new function by [tex] u1(t) = u(x1(t),t). [/tex] For example, if x1 is function giving the position of electron, u1 gives the electric field acting on the electron at time t. However, the function x1 has to be inferred from other sources; there is nothing in the wave equation that would give such a function. True, there is the motion of the maxima of the wave crests and one could ascribe such function x1(t) to one of them, but there is no good reason for doing so  there is no particle there  so it would seem to be just an empty exercise. 


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