sol4 - PHYS 218 - SOLUTION TO ASSIGNMENT 4 23 Feb 2007 By...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PHYS 218 - SOLUTION TO ASSIGNMENT 4 23 Feb 2007 By Chung Koo Kim e-mail : ck269@cornell.edu 1. String with a massive bead Lets suppose that the sinusoidal wave is incoming from the left. The wave equations of left and right side of the mass can be written left = e ikx + Re- ikx right = Te ikx so that the left has both incoming/reflected components and right has only outgoing transmitted component. Remarks. The following forms may be more general and familiar: left = A 1 e i ( kx- t ) + B 1 e- i ( kx + t ) right = A 2 e i ( kx- t ) Pay attention to the signs of kx and t . Waves propagating toward the positive x direction should have opposite sign for kx and t , and same sign for negative x direction. And we may replace the i in the above equation by- i without loss of generality at least for our purpose. But for later consistencys sake, particularly in quantum mechanics, we keep + ikx for wave toward (+x) and- ikx for (-x). You will learn that e ikx has positive momentum when we apply momentum operator p = h i x . And since we are mostly interested in the relative ratio of the coefficients only, we divide the equation by A 1 and replace B 1 /A 1 = R and A 2 /A 1 = T . Of course we took the common factor of e it out. Then we get the first set of equations. To match the two solutions at x=0, we should find two boundary conditions: left ( x = 0) = right ( x = 0)- left x x =0 + right x x =0 = m 2 right t 2 The first one comes from the continuity of the string, and the second one from Newtons second law applied to the vertical component of force. The ( x, t ) in the second equation can be either left ( x, t ) or right ( x, t ) since the two are the same at x=0. Note that we are in practice thinking of the limit approaching zero from the left and right, when plugging x=0....
View Full Document

This note was uploaded on 03/13/2008 for the course PHYS 2218 taught by Professor Wittich,p during the Spring '08 term at Cornell University (Engineering School).

Page1 / 5

sol4 - PHYS 218 - SOLUTION TO ASSIGNMENT 4 23 Feb 2007 By...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online