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Superposition and Interference
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Review of Superposition Two sound waves arriving at the same point P: Pressure fluctuations Resulting pressure fluctuation at P +
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Signal at P p(t) time t
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Signal at P: constructive interference p(t) time t The sound wave is enhanced Δt=n*τn=…-2,-1,0,1,2,… any whole number When will this happen? Δt= -τ Δt= 2τ Δt= 0
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Signal at P: destructive interference p(t) time t The sound wave is canceled out. Δt=(n+1/2)*τn=…-2,-1,0,1,2,… any whole number When will this happen? Δt=-1/2*τΔt=+1/2*τΔt=-τ-1/2*τ
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Superposition Constructive interference: The wave is enhanced if Destructive interference: The wave is canceled if
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In space: Lines of constructive interference ΔL=nλ (maxima and minima arrive at same time at points on these lines)
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In space: Lines of destructive interference ΔL=(n+1/2)λ (maxima of one wave and minima of the other arrive at same time at points on these lines)
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Path length diffence Two rays traveling parallel. How many rays are there coming from a point source? ΔL=0 ΔL=1.5λ
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Better… Use overhead projector for demonstration
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