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Simplification about the reflection of waves at a discontinuity.

  1. Apr 16, 2012 #1
    The following reffers to the reflection of waves at a discontinuity. (incident, reflected, and transmitted waves)

    1. The problem statement, all variables and given/known data

    (a) Simplify Aicos(k1x-wt)+Arcos(k1x+wt) = Atcos(k2x-wt) by eliminating common trig factors (recall cos(-θ)=cos(θ)), and dividing terms by Ai to express the resulting equation in terms of r=Ar/Ai and τ=At/Ai.
    (b) Substitute Aicos(k1x-wt)+Arcos(k1x+wt) = Atcos(k2x-wt) into cd5c40da-02e0-4b0d-89b9-a879927e4c9d.png , eliminate common trig factors (recall sin(-θ)=sin(θ)), divide terms by k1Ai, and express the resulting equation in terms of r and τ as before. (the ratio k2/k1 should also appear in your result, the refracting index)
    (c) By treating your resulting equations in parts (a) and (b) as two equations in two unknowns r and τ, find separate expressions for r and τ involving ONLY the refractive index n=k2/k1.


    2. Relevant equations

    yi(x,t)=Aicos(k1x-wt)
    yr(x,t)=Arcos(k1x+wt)
    yt(x,t) = Atcos(k2x-wt)
    sin(-θ)=sin(θ)
    cos(-θ)=cos(θ)

    3. The attempt at a solution
    This was a problem about reflection of waves at a discontinuity. (incident, reflected, and transmitted waves). I solved everything up to this point, and re-wrote the question.
     
  2. jcsd
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