Discontinuity Waves: Deriving the expressions

[Showaddywaddy]

Homework Statement

A long string of linear mass density μ_1 = 1.0 gr/cm is joined to a long string of linear mass density μ_2 = 4.0 gr/cm and the combination is held under constant tension. A transverse sinusoidal wave of amplitude A _i = 3.0 cm and wavelength λ =25 cm is launched along the lighter string.


Q. Derive the expressions for the incident, transmitted and reflected waves.

Homework Equations

y (x,t) = A \sin(k x -\omega t)

v = \sqrt {\frac {T}{μ}}

The Attempt at a Solution

Is there a way to derive the expressions mathematically? I know the reflected wave will have the same constant K as the incident wave but will be traveling to the left rather than the right and the transmitted wave will have a different k value than the incident wave but will be traveling to the left.

This is as far as I have gotten with the problem as I can write the expressions from them conclusions but not giving an expression for the amplitudes of the transmitted and reflected waves in terms of the incident wave or waves for the k constants.

 

[HallsofIvy]

You are clearly expected, in this problem, to be able to find formulas for a wave on a string with constant density. Do that for each string, separately, the determine the conditions where the two strings meet.