Superposition of Waves

Superposition of water waves http://www.ngsir.netfirms.com/englishhtm/Interference.htm

Electric field of electromagnetic wave by dipole oscillator

e0 : permitivity of free space m0: permeability of free space Maxwell’s wave equation in free space

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

Wave Superposition © 1997-2006 Edward A. Zobel http://id.mind.net/~zona/mstm/physics/waves/interference/waveInterference1/WaveInterference1.html

Addition of wave of same frequency Algebraic method Complex method Phasor addition

Algebraic method of Addition

where,

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

For

Flux density

The phase difference between two interfering waves

Superposition of many waves

Complex method of Addition

Resultant of N waves

Complex amplitude of the resultant wave

For N=2

Phasor Addition of Waves

Argand Diagram Representation of a complex number in terms of real and imaginary components In Complex plane A Sin wt A Cos wt Re

Rotating Arrow + Associated Phase Angle = Phasor

Addition of two phasor Resultant

Addition of three phasor

Find A and f

Problem Superposition of large number of phasors of equal amplitude a and equal successive phase difference f. Find the resultant phasor.

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