# waves_02 - waves_02 1 SUPERPOSITION OF WAVES Two waves...

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1 Two waves passing through the same region will superimpose - e.g. the displacements simply add Two pulses travelling in opposite directions will pass through each other unaffected While passing, the displacement is simply the sum of the individual displacements CP 514 SUPERPOSITION OF WAVES waves_02 Animations courtesy of Dr. Dan Russell, Kettering University

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2 waves_02: MINDMAP SUMMARY – SUPERPOSITION PRINCIPLE Travelling waves, superposition principle, interference, constructive interference, destructive interference, intermediate interference, nodes, antinodes, phase, phase difference, in phase, out of phase, path difference, two point interference, standing waves on strings, standing waves in air columns, thin film interference 1 2 ( , ) ( , ) ( , ) o o o y x t y x t y x t = + Superposition (at time t o ) Wave 1 + Wave 2 Constructive interference: = m λ m = 0, 1, 2, 3, . .. ∆φ = m (2 π ) Destructive interference: = ( m + 1/2) λ ∆φ = ( m + ½) (2 π ) 14 15
3 0 4 8 12 16 20 24 28 0 10 20 30 40 50 60 70 80 90 CP 510 SUPERPOSITION INTERFERENCE In phase constructive interference Out of phase destructive interference

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4 Problem 1 Two sine waves travelling in the same direction Constructive and Destructive Interference Two sine waves travelling in opposite directions standing wave
5 Interference of two overlapping travelling waves depends on: * relative phases of the two waves * relative amplitudes of the two waves fully constructive interference: if each wave reaches a max at the same time, waves are in phase (phase difference between waves two waves ∆φ = 0) greatest possible amplitude ( y max1 + y max2 ) fully destructive interference:

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## This note was uploaded on 09/01/2011 for the course YEAR 1 taught by Professor Various during the Three '11 term at University of Sydney.

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waves_02 - waves_02 1 SUPERPOSITION OF WAVES Two waves...

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