Superposition and Interference. Review of Superposition Two sound waves arriving at the same point P: Pressure fluctuations Resulting pressure fluctuation.

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Presentation transcript:

Superposition and Interference

Review of Superposition Two sound waves arriving at the same point P: Pressure fluctuations Resulting pressure fluctuation at P +

Signal at P p(t) time t

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

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

Superposition Constructive interference: The wave is enhanced if Destructive interference: The wave is canceled if

In space: Lines of constructive interference ΔL=nλ (maxima and minima arrive at same time at points on these lines)

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)

Path length diffence Two rays traveling parallel. How many rays are there coming from a point source? ΔL=0 ΔL=1.5λ

Better… Use overhead projector for demonstration