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Transmission of mechanical wave on two different ropes

  1. Jul 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Two infinite ropes, rope 1 and rope 2, of same linear density ##\mu=0.1 kg/m## have the same tension ##T=100N## and lie on the same plane, one perpendicular to the other. The two ropes are connected in the origin. On one of the two branches of rope 1 an harmonic wave is travelling towards the origin. The oscillation are perpendicular to the plane of the ropes with amplitude ##A=3cm## and frequency ##f=5 Hz##. Determine
    a) wavelenghts, frequencies and velocities of transmitted and reflected waves
    b) amplitudes of transmitted and reflected waves
    c) average power of transmitted and reflected waves

    2. Relevant equations
    Reflection and transmission coefficients for mechanical waves, see here https://cnx.org/contents/IEH5M2Ue@2/Reflection-and-Transmission-of

    3. The attempt at a solution
    a) Since ##\mu## and ##T## are the same for all rope, the velocities and wavelenghts are all the same for all the waves (frequency would be the same in any case)

    The problem is that I cannot really figure out what happens for points b) and c).

    What I'm quite sure about is that there is no reflected wave on the branch where the wave is coming from, because the coefficient of reflection is zero, since ##\mu## is the same in all the rope 1. I'm also quite sure that there is a transmitted wave.

    But are waves generated on rope 2? If so, how to find aplitudes and powers?
     
  2. jcsd
  3. Jul 13, 2016 #2

    Orodruin

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    The reflection coefficient is not going to be zero because the additional ropes are going to affect the transversal force balance in the node. You need to find the proper boundary conditions at the node and use them to determine what is going on.
     
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