# lecture30 - Superposition of Waves Text sections 18.1-18.4...

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Text sections 18.1 Text sections 18.1 -18.4, 18.7 18.4, 18.7 (next 3 lectures) (next 3 lectures) 1) Identical waves in opposite directions: “standing waves” 2) 2 waves at slightly different frequencies: “beats” 3) 2 identical waves, but not in phase: “interference” Superposition of Waves Practice ( for today’s topics): Chapter 18, problems 1, 2, 3, 5, 11. Principle of Superposition Principle of Superposition When two waves meet, the displacements add: ) , ( ) , ( ) , ( 2 1 t x y t x y t x y + = observed So, waves can pass through each other: v (for waves in a “linear medium”)

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Quiz Quiz v v Sketch the particle velocities at the instant the string is completely straight. Principle of Superposition Principle of Superposition 2 Waves In The Same Medium : The observed displacement y ( x,t ) is the sum of the individual displacements: y 1 ( x,t ) + y 2 ( x,t ) = y ( x,t ) (for a “linear medium”)
2 waves, of the same frequency ; arrive out of phase: Eg. ) sin( ) sin( 2 1 φ ω + = = t kx A y t kx A y Trigonometry: sin a + sin b = 2 cos [(a-b)/2] sin [(a+b)/2] Result:

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lecture30 - Superposition of Waves Text sections 18.1-18.4...

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