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Unformatted text preview: 1 Physics 1B Class Notes © Week 3 Walter Gekelman Chapter 16  University Physics Interference: Consider waves emanating from S 1 and S 2 as in the diagram below. They could be sound waves or water waves or light waves. If both waves travel the exact same distance to point P they will arrive in phase and the amplitudes will add. Recall the waves can be represented as: y = Ae i kx − ω t ( ) + Ae i kx + ω t + δ ( ) = Ae i kx − ω t ( ) 1 + e i δ ( ) If there is no phase difference: y = Ae i kx − ω t ( ) 1 + e i δ ( ) = Ae i kx − ω t ( ) 1 + e i ( ) = 2 Ae i kx − ω t ( ) ; δ =0 If however there is a path difference and the waves travel different distances to get to P there will be a phase difference which is, in fact Why is this so. δ = 2 π λ path difference ( ) If P is moved slightly to the side P ! S 1 S 2 When ! = n " /2 the wave are out of phase and cancel at point P Two sources each broadcast waves at the same frequency 2 and the path difference becomes one wavelength then the phase difference will be 360 degrees (2 π ) and the result is the same as above. If the difference is π then the waves will interfere giving a null. How do we see this… y = Ae i kx − ω t ( ) 1 + e i δ ( ) = Ae i kx − ω t ( ) 1 + e i π ( ) ; δ = π e i π = cos π + i sin π = − 1 y = Ae i kx − ω t ( ) 1 − 1 ( ) = The waves destructively interfere. The pattern is shown in the figure to the right The sources S1 and S2 are the red spots in the center. The bright sections are places where the waves are maxima (crests) and the black regions where there are minima (troughs) interference is positive. The grey regions are where the amplitude is zero and there is “destructive” interference. If there were water waves and you were on a boat on a grey region you would not bob up and down. 3 Sound Sound is a longitudinal wave. Sound is a longitudinal wave....
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 Spring '10
 gekelman
 Force, Fundamental physics concepts

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