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Height And Width of Reflected Pulses (through less dense medium) ?

  1. Jul 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider the waveform shown below heading towards a boundary between two
    strings. Let string 1 have mass per unit length of µ1 = 0.05 kg/m and let string 2
    have a mass per unit length µ2 = 0.02 kg/m. Let the tension in both strings be T
    = 100N.
    -->
    ____/\____ _ _ _ _ _ _ _
    string 1 ... string 2

    Using the reflection and transmission coefficients, sketch the reflected and
    transmitted pulses after the incident pulse has completely passed through the
    boundary. How do the width and height of the reflected and transmitted pulses
    compare to the incident pulse?

    2. Relevant equations

    (Ar + Ai) * cos(wt) = At * cos(wt)
    Ai + Ar = At
    k(1) * (Ar - At) = -k(2) * Atr

    3. The attempt at a solution

    r = (v(2) - v(1)) / (v(2) + v(1))
    τ = 2*v(1) / (v(1) + v(2)) = 2 / (1 + v(1) / v(2))
    v(2) = sqrt( (f * τ) / µ2 ) & vise versa
    v(1) / v(2) = sqrt( µ2 /µ1 )
    r = (1-0.63)/(1+0.63) = 0.225, t= 1.225

    I know the pulse in the lighter string should look like ___ _ /\ _ _ (taller but less wide)

    But how do I quantitatively illustrate that the width and height change, and by how much?

    Help is definitely appreciaTed!
     
  2. jcsd
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