Cartesian Co-ordinates of Plane Wave

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Write an expression in Cartesian coordinates for a plane wave of amplitude A and frequency ω propagating in the direction of the vector k which, in turn, lies on a line drawn from the origin to the point (4,2,1).



Well, we know plane wave is E(r,t)= E*e^(i(kr –ωt)) where E = A*(direction of propagation) for a 3D wave. However, we're not entirely sure where to go now. One of our friends believes it should just be A*e^(i(kr –ωt)), ie just the amplitude , not propagation as above. We also think that it might be E*e^(i(4x+2y+z –ωt)), as k*r should equal 4x+2y+z. Are we anywhere near being along the right lines?
 

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  • #2
Meir Achuz
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No.
k.r means xk_x+yk_y+zk_z.
You need to find the components of k.
k_x=4k/sqrt(21), etc.
 

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