PHY4604 R. D. Field Department of Physics Chapter1_4.doc University of Florida Re(Ψ)A Ψ= Aei(kx-ωt)Im(Ψ) φ = kx-ωtt Im(Ψ) = Asin(kx-ωt)AACrest TroughA Ψ(0,t) = Ae-iωtDistance r φ = kr-ωtx = 0 φ =-ωtA x = r Ψ(r,t) = Aei(kr-ωt)Representing Waves as Complex Numbers We can use complex numbers to represent traveling waves. If we let)(tkxiAeω−=Ψthen )cos()Re(tkxAω−=Ψis a traveling plane wave with wave number k = 2π/λ, “angular” frequency ω= 2πf, and amplitude A. The intensity, I, is proportional to A2. ∗ΨΨ=Ψ=A22Ψ=∝AIPhase-Shift Due to a Path Length Difference Consider two traveling wave that are in phase at their source, but
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