Physics Problem help?

Posted on 2017-03-09 18:20:00 in Physics by RICHARD

Two strings of linear mass density mu(1) and mu(2) are connected end-to-end with a knot. Let the knot's position be designated as x = 0, and that both strings are stretched to the common tension magnitude F. A wave, described by the function y = A(k1(x - v1t)), initially propagates through the string of density mu(1). Upon reaching the junction between the 2 strings, it is partially transmitted into the string of density mu(2) and partially reflected backwards; call these 2 wave functions yt = Bsin(k2(x - v2t)) and yr = Csin(k1(x + v1t)). 

a) Assuming that k2v2 = k1v1 = W and that the displacement of the knot arising from the incident and reflected waves is the same as that arising from transmitted wave, prove that A = B + C.

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