# Chp41_4 - PHY2061 R D Field Representing Waves as Complex Numbers = Aei(kx t Im = Asin(kx-t Crest Im A A = kx t Re t A Phase Wave Function Trough

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PHY2061 R. D. Field Department of Physics chp41_4.doc University of Florida Re( Ψ ) A Ψ = Ae i(kx- ω t) Im( Ψ ) φ φ = kx- ω 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 = then ) sin( ) 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 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 wave 1 travels a distance
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## This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.

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