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Lecture 8 Notes - Recap of last lecture Instantaneous power...

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Recap of last lecture Max Power 2 2 A ω μF = Average power = ½ Max power Instantaneous power ωt) (kx sin A ω μF 2 2 2 - = Intensity = Power per unit area W/m 2 Waves reflect at boundaries (changes in medium) If Particles at the boundary are: Fixed (feel a transverse force) – 180 0 phase shift Free (no transverse force) - 0 0 phase shift Reflection from low to high density medium – 180 0 Reflection from high to low density medium - 0 0 I 1 /I 2 = r 2 2 /r 1 2
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Recap of last lecture Superposition of waves: y(x,t) = y 1 (x,t) + y 2 (x,t) (linear superposition) Superposition special case: standing waves , when two waves have the same amplitude and frequency, but are traveling in opposite directions (and a phase difference of 180 0 ) Amplitude 2 x incident wave sine wave shape Sine wave oscillation in time but confined to same location y SW (x,t) = (2Asinkx)sin ϖ t Nodes (where the two waves cancel out) when sinkx = 0 or kx = 0, π ,2 π , 3 π ,… or x = 0, λ /2, λ , 3 λ /2, … Anti-nodes (where the two waves add) when sinkx = 1 or kx = π /2,3 π/2 ,5 π/2 ,7 π/2 ,… or x = λ /4, 3 λ/4 , 5 λ /4, …
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Normal Modes of Strings
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