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class14lecnotes - Class 14, WeJ01JItf ,February 10, 2010...

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Class 14, WeJ01JItf ,February 10, 2010 Reading: lit, 7- Review !j(X1t):: It51n./~X-CJt) ./2;; CJ:: 2/;- ) / ~(Ylt):: A·fln. (kk+wt) / = ( T /\ T 2 Of I:: .!:d 2ii /; ~'I" U Ii I ..- - T V·I. ... {I· ~ 2 l or :: -:: --,- I Zif Vr - z T !f~ / (Nxl/liJ!) The Principle of Superposition Last Friday, we talked about and described a single traveling wave. What happens when two traveling waves meet? We are, all very familiar with the consequence of two of us trying to be in the same place at the same time. We know this is bad news.
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(/JtJ f iON If!~) Example 1 A long string with f,A.=2g/m is stretched along the x-axis with a tension of 5 N. At x=O it is forced to oscillate at a frequency of 100 Hz perpendicular to the x-axis. The amplitude of this oscillation is 2 mm. The oscillation is at a maximum positive displacement at t=o1 e ~ )( ~O ) a) Write the wave equation for the traveling wave on the string. b) At t=5 ms, what is the string's displacement at a point 2.7 m from x=O? L a) IJ· ~ fl<x - ()Jt -1- C/b) !j /'1 It} :: ~ hv jor'Cli (//c/tldtlVf. cJ t1~O JtMtArdid lIuJ If /tr)(/t.i<M; ~, a ;l=.2~ W = ~ == :2 if / '" ~ (}() /; r«dls T ~ ~ 2/1 7< - ). 51': ), <r '" > MHJ 1/1/ -:::)~:-. /d(J ;} .rift__ ; d. $7J.A-. ,2')O-l)j/hl llw=/Ji ~) IIVr:J~i · =--/ k:::l!!- = 4-1/ Tud/tAA. . (). riP
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When two of us try to be in the same place at the same time, things don't work out. Energy is being dissipated. Waves, however, have no problem being at the same place at the same time. When waves do this, energy is conserved. Wby can waves do it and we can't? Waves are not material. They are simply distributions of energy that perturb the matter through which they run. Because of this, in order to find their resultant contribution, waves can simply be added up at any point where they meet. When two or more waves meet at one point in space, the total displacement of the medium at this point is the sum of the individual displacements of each wave. This is called the superposition principle. When two waves have a maximum displacement at a given point, the resuirant displacement is the sum of the contributions of the two individuals. If one wave has a given positive displacement, while the other has a negative displacement of equal. f'/Itljn/1£dL.
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class14lecnotes - Class 14, WeJ01JItf ,February 10, 2010...

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