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lec12a-203-11-standwaves

# lec12a-203-11-standwaves - Wave Superposition Waves of...

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Ph203:20-6A Waves of small amplitude traveling through the same medium combine, or superpose, by simple addition. Wave Superposition 12a-1

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Principle of Linear Superposition f Tot = f 1 (x v t) + f 2 (x v t) Ph203:20-7 Wave Interference 12a-2
10-3 8-2 recall 12a-3

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Aside: M. Fourier proved that any (well behaved) wave* can be written as a sum of simple harmonic waves. square wave triangle wave can handle “anything” just add up enough SH waves SH waves are all we need Flip-side: one can break down any wave into Fourier SH components # of sine waves summed 12a-4
v = wave velocity 0 + - Add up 2 waves point by point Interference – partial/total cancelation/increase Constructive Interference = + Destructive Interference = + 0 anything in-between 8-3 Interference: simple harmonic waves 12a-5

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2 identical waves traveling in opposite directions 12a-6 t x t x sin(2π + 2π )+ sin(2π - 2π ) TT AA  Sum= t -2πx sin(2π ) cos( ) T A Sum= 2 trig. identity Standing wave + vs only difference time only space only
/2 0 to 0 |max| to |max| /4 /2 Note: same 12a-7

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Standing Waves: e.g. string with
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lec12a-203-11-standwaves - Wave Superposition Waves of...

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