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Superposition of Waves
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Superposition of water waves
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Electric field of electromagnetic wave by dipole oscillator
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e0 : permitivity of free space
m0: permeability of free space Maxwell’s wave equation in free space
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PRINCIPLE OF SUPERPOSITION
The resultant disturbance of any point in a medium is the algebraic sum of the separate constituent waves. ‘s are solution of linear differential wave equation
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Wave Superposition © 1997-2006 Edward A. Zobel
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Addition of wave of same frequency
Algebraic method Complex method Phasor addition
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Algebraic method of Addition
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where,
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The composite wave is (ii) of same frequency as that of constituents
(i) harmonic (ii) of same frequency as that of constituents (iii) of different amplitude and phase from that of constituents
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For
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Flux density
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The phase difference between two interfering waves
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Superposition of many waves
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Complex method of Addition
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Resultant of N waves
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Complex amplitude of the resultant wave
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For N=2
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Phasor Addition of Waves
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Argand Diagram Representation of a complex number in terms of real and imaginary components In Complex plane A Sin wt A Cos wt Re
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Rotating Arrow + Associated Phase Angle = Phasor
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Addition of two phasor Resultant
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Addition of three phasor
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Find A and f
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Problem Superposition of large number of phasors of equal amplitude a and equal successive phase difference f. Find the resultant phasor.
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Summary The composite wave is
(i) harmonic (ii) of same frequency as that of constituents (iii) of different amplitude and phase from that of constituents
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