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12 Waves 3 - When two(or more waves of the same kind...

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When two (or more) waves of the same kind propagate through the same region, they produce a composite wave. This phenomenon is called interference . It is constructive , when the waves reinforce each other. It is destructive , when they reduce each other’s amplitude. Usually the disturbances (displacements) the waves produce are added algebraically . This is called superposition principle.
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Superposition principle: adding two square waves + ?
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Superposition principle: adding two harmonic waves + ?
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Superposition of pulses: Constructive Interference
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Superposition of pulses: Destructive Interference For a moment it the string becomes a straight line – no disturbance is seen. Does the energy of wave motion disappear? Where does it go? How can the two waves go on after that? Two kinds of energy in the wave motion: potential – depends on deflection of the string from the straight line; kinetic – depends on velocity of motion of the string. In the very moment, when the string becomes straight, it is actually moving very fast - high K .
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http://www.kettering.edu/~drussell/Demos/superposition/superposition.html
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When there are two interfering waves with close but different frequency the result of the interference is the beats . They are perceived as a wave with an average frequency , but with a slowly oscillating amplitude .
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When there are two interfering waves with close but different frequency the result of the interference is the beats . They are perceived as a wave with an average frequency , but with a slowly oscillating amplitude . ] ) ( 2 1 cos[ ] ) ( 2 1 cos[ 2 ) ( 2 1 2 1 t t A t y ω ω ω ω + = ) cos( ) ( 1 1 t A t y ω = ) cos( ) ( 2 2 t A t y ω = ) cos( ) cos( ) ( ) ( ) ( 2 1 2 1 t A t A t y t y t y ω ω + = + = The resulting composite wave:
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When there are two interfering waves with close but different frequency the result of the interference are beats.
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