Lecture 28

# Lecture 28 - Interference Phenomea The two main things you...

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Interference Phenomea The two main things you need to know: 1. Two equal-amplitude coherent waves that reach a point with a phase difference of 2 π n or a path difference of n λ , where n is any integer, constructively interfere . The resultant wave has twice the amplitude of either constituent wave, and four times the intensity . 2. Two equal-amplitude coherent waves that reach a point with a phase difference of 2 (n+1/2) or a path difference of (n+1/2) , where n is any integer, destructively interfere . The resultant wave has zero amplitude and zero intensity .

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Constructive/Destructive • Constructive: peaks align with peaks, valleys aligns with valleys. • Destructive: peaks align with valleys; valleys align with peaks.
Beats, Phase difference from frequency difference Suppose we have two sources of equal amplitude and slightly different frequency at the same location. We’ll show that for E 1,2 =E 0 cos(2 π f 1,2 t), that the resultant field is E 1+2 =2E 0 cos[2 π (f 1 - f 2 )t/2]cos[2 π (f 1 +f 2 )t/2]. For small |f 1 -f 2 |, the factor cos[2 π (f 1 - f 2 )t/2] modulates the amplitude rather than contributing any tone.

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• Consider two nearly point-like wave sources as shown in the figure. White represents peaks, black valleys. • Along a line far from the sources, whites cross blacks at nearly equal intervals. These will be positions of interference minima. • A similar effect occurs for white crossing white and black
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Lecture 28 - Interference Phenomea The two main things you...

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