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Unformatted text preview: The University of Western Australia School of Electrical, Electronic and Computer Engineering Solutions - Tutorial Sheet 15, 2006 Electromagnetic Theory ENGT3303 Question 1 The resulting plane wave is obtained by superposition and is given by ( ) ( ) ( ) z t A z t A t z 2 2 1 1 cos cos , β ω β ω − + − = Ψ If we substitute in the four equations for ω 1 , ω 2 , β 1 , and β 2 , as given in the question and use the identity ( ) β α β α β α sin sin cos cos cos m = ± , the resultant wave becomes ( ) ( ) ( ) z t z t A t z β ω β ω − ∆ − ∆ = Ψ cos cos 2 , This resultant wave is a carrier wave at frequency ω = ω 1 + ω 2 ( ) / 2 and phase velocity v = ω / β . The amplitude of the carrier wave is a wave of frequency ∆ ω , called the beat frequency, and propagation constant ∆ β traveling at velocity v g = ∆ ω / ∆ β . time group carrier This velocity is called the group velocity, and represents the rate of flow of energy....
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This homework help was uploaded on 04/17/2008 for the course ELEC 3305 taught by Professor - during the Spring '07 term at W. Alabama.
- Spring '07