lecture28 - Superposition of Waves Superposition of Waves...

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Superposition of Waves
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1) Identical waves in opposite directions: “standing waves” 1) 2 waves at slightly different frequencies: “beats” 1) 2 identical waves, but not in phase: “interference” Superposition of Waves
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Principle of Superposition Principle of Superposition 2 Waves In The Same Medium : The observed displacement y ( x,t ) is the algebraic sum of the individual displacements: y ( x,t ) = y 1 ( x,t ) + y 2 ( x,t ) (for a “linear medium”)
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2 waves, of the same amplitude, same angular frequency and wave number (and therefore same wavelength) traveling in the same direction in a medium but are out of phase: ) sin( ) sin( 2 1 φ ϖ + - = - = t kx A y t kx A y Trig: sin a + sin b = 2 cos [(a-b)/2] sin [(a+b)/2] Result: + - = + = 2 sin 2 cos 2 2 1 t kx A y y y Resultant amplitude What’s Special about Harmonic Waves?
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For what phase difference is the total amplitude 2A? For what phase difference
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lecture28 - Superposition of Waves Superposition of Waves...

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