Question

The end of a long string of mass per unit length µ is knotted to the...

The end of a long string of mass per unit length µ is knotted to the beginning of another long string of mass per unit length µ0 . The tensions in these strings are equal. A harmonic wave travels along the first string toward the knot. This incident wave will be partially transmitted into the second string, and partially reflected. The frequencies of all these waves are the same. With the knot at x = 0, we can write the following expressions for the incident, reflected, and transmitted waves:

y1(t) = Ain cos(kx − ωt)

y2(t) = Aref cos(kx + ωt)

y3(t) = Atrans cos(k0 x − ωt) .

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