PHY4604 R. D. Field Department of Physics Chapter1_4.doc University of Florida Re( Ψ ) A Ψ = Ae i(kx-ω t) Im( Ψ ) φ = kx-ω t t Im( Ψ ) = Asin(kx-ω t) A A Crest Trough A Ψ (0,t) = Ae-i ω t Distance r φ = kr-ω t x = 0 φ =-ω t A x = r Ψ (r,t) = Ae i( kr-ω t) Representing Waves as Complex Numbers We can use complex numbers to represent traveling waves. If we let ) ( t kx i Ae ω − = Ψ then ) cos( ) Re( t kx A − = Ψ is a traveling plane wave with wave number k = 2 π / λ , “angular” frequency ω = 2 π f , and amplitude A . The intensity, I , is proportional to A 2 . ∗ ΨΨ = Ψ = A 2 2 Ψ = ∝ A I Phase-Shift Due to a Path Length Difference Consider two traveling wave that are in phase at their source, but
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