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Unformatted text preview: PHYSICS 218 SOLUTION TO HANDOUT 5 Created: September 19, 2004 10:02pm Last updated: September 19, 2004 11:34pm Fixed and free boundary conditions. Lets consider a transverse sinusoidal wave travelling on a string consisting of two parts, where the left part has a linear density 1 and the right part a different linear density 2 , but with both parts under the same tension (our good old Newtons Laws still work here!). For convenience, the origin is chosen at the discontinuity x = 0, and a source on the negative x-axis sends waves towards the discontinuity. We have seen that the reflection and transmission coefficients of waves at a discontinuity are given by R = k 1- k 2 k 1 + k 2 , T = 2 k 1 k 1 + k 2 , (1) where k 1 and k 2 are the magnitude of the wave vectors to the left and right of the discontinuity, respectively. 1. Show that R and T can be written in the form R = v 2- v 1 v 2 + v 1 , T = 2 v 2 v 2 + v 1 , (2) where v 1 and v 2 are the magnitude of the wave velocities to the left and right of...
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