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Progressive harmonic wave & reflection / transmission

  1. Sep 22, 2015 #1
    1. The problem statement, all variables and given/known data
    An incident wave frequency f =500Hz , power Wi = 50 W and amplitude Ai= 5 mm spreads to the positive x in a linear density rope u1 unknown. When the wave encounters another rope ( attached to the first at a point P) density linear u2= 64 g/m (such as u2>u1 ) , The transmitted wave has a power Wt = 32 Watts.

    a) Determine u1, and the value of the impedance Z1 and Z2.

    2. Relevant equations


    3. The attempt at a solution
    64g/m = 0.064kg/m
    5 mm = 0.005 m

    T = Wt/Wi
    T= 32/50
    T = 0.64

    R + T = 1 => R + 0.64 = 1
    R = 0.36
    R = r2
    0.36 = r2
    r = 0.6

    Ar = r*Ai
    Ar = 0.6 * 0.005
    Ar = 0.003

    sqrt(u1)/sqrt(u2) = (Ai + Ar)/ (Ai - Ar)
    sqrt(u1)/sqrt(0.064) = (0.005 + 0.003)/ (0.005 - 0.003)
    u1 = 0.1024

    Something is wrong and I cant figure it out, I know its wrong because it says u2 has to be bigger than u1, and my answer of u1 is bigger than u2.

    thanks.
     
  2. jcsd
  3. Sep 26, 2015 #2

    Simon Bridge

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    Show your reasoning at each stage in the calculation.
     
  4. Sep 26, 2015 #3
    I resolved this problem, I do not need help.
     
  5. Sep 27, 2015 #4

    Simon Bridge

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    You can help others if you show how you solved the problem.
     
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