Lecture21 - Lecture 21: Superposition, Interference, and...

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Lecture 21: Superposition, Interference, and Light Waves Last time we introduced the principle of superposition, which explains what happens if many waves are traveling in the same medium i.e., several waves on the same string, or several sources of sound in the same room The medium responds to the sum of all the waves: Consider two waves with the same amplitude and frequency, but different values at x = t = 0 this value is known as the phase of the wave y x , t ( 29 = ψ 1 ξ,τ ( 29 + ψ 2 ( 29 + Κ + Ν ( 29
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The nature of the resulting wave depends on φ Special cases: 1. φ = 0: 1. φ = 180 o : y 1 x , t ( 29 = Ασιν κξ -ϖτ ( 29 ψ 2 ξ,τ ( 29 = Ασιν κξ -ϖτ+ φ ( 29 y x , t ( 29 = Α σιν κξ -ϖτ ( 29 + σιν κξ -ϖτ+ ( 29 = Α σιν κξ -ϖτ ( 29 + σιν κξ -ϖτ ( 29 χοσφ + χοσ κξ -ϖτ ( 29 σινφ ( 29 1+ χοσφ ( 29 + χοσ κξ-ϖτ ( y x , t ( ( 29 1 ( 29 + χοσ κξ -ϖτ ( 29 0 ( 29 = 2Ασιν κξ -ϖτ ( 29 y x , t ( ( 29 1-1 ( 29 + χοσ κξ -ϖτ ( 29 0 ( 29 = 0 Twice the amplitude of the original wave No wave at all! Phase
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Interference in Two Dimensions If waves are traveling in more than one dimension (across the surface of water, for example) even more interesting patterns of interference can result Assume we have two identical wave sources lines below represent wave crests When two crests (or troughs) overlap, get a large amplitude (constructive interference) When a crest overlaps a trough, get small amplitude (destructive interference)
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We can tell whether a given point in space will have a maximum or minimum of the amplitude by finding the distance from that point to each source ( d 1 and d 2 )
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Lecture21 - Lecture 21: Superposition, Interference, and...

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