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Chapter 16 4 Superposition 4 and 4 Standing Waves

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Section 16-1: Superposition of Waves When two or more waves combine, the resultant wave at any point, is the algebraic sum of the individual waves.

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Superposition and the Wave Equation y 3 = c 1 y 1 + c 2 y 2 superposition

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Interference of Harmonic Waves

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Constructive interference

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Destructive Interference

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Beats

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Phase difference due to a path difference Waves are in phase if the phase difference, δ= n(2π) This results in constructive interference

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The waves are exactly out of phase when δ= (n+½)2π This results in destructive interference

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Example 16-2 p 485

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Intensity versus path difference for two sources that are in phase.

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Two sources that are in phase, or have a constant phase difference are said to be coherent. The Double Slit Experiment: doubleslit

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Section 16-2: Standing Waves String fixed at both ends The standing wave condition is when L = n(½λ) and f n = nν/2L =nf 1

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A classic Steinway piano

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String fixed at one end.

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Wave functions for standing waves String fixed at both ends wavesuperposition

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String fixed at one end

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Standing sound waves on the surface of the sun

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Some of the many modes of oscillation of a ringing handbell

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