PHYS 422 Lecture 2 Wave Motion I

PHYS 422 Lecture 2 Wave Motion I - Chapter Chapter 2 Wave...

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hapter 2 Chapter 2 ave otion I Wave Motion I
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One Dimensional Wave Classical traveling wave: self-sustaining disturbance of a medium, which moves through space transporting energy and momentum. Example: sound waves ongitudinal waves: Longitudinal waves: the medium is displaced in the direction of motion Transverse waves: the medium is displaced in the direction perpendicular to motion Note: disturbance advances, not matter
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One Dimensional Wave The disturbance, ψ , must be a function of both position and time: () ( ) t x f t x , , = The shape of the disturbance at any instant is the profile of the wave: ) ( 0 , , 0 x f x f t x t = = = at time = 0
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Special case: One Dimensional Wave the shape of the wave does not change in time Assume: td ( ) ( ) 2 exp ax x f = ‘Gaussian function’ - wave moves at speed v - at time t= 0 its profile is f ( x ) t time e disturbance has moved a distance At time t the disturbance has moved a distance v t along the x axis, but its shape is the same: ( ) ( ) t x f t x v = , ψ ( ) [ ] 2 exp t x a v = If we have a snapshot of a wave shape at time zero we can find a full time- dependent equation of the wave. () ( ) t x f t x v + = , What is this?: Regardless of the shape, the variables x and t must appear as a single unit ( v t )
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Differential Wave Equation i th ti i th ti f th tt Fix the time in the equation for the wave ψ ( x,t=const ) - get the shape of the wave in space Fix in the equation for the wave =const,t x t e equat o o t e wave ( x const,t ) - get the dynamics of the disturbance at a particular coordinate
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PHYS 422 Lecture 2 Wave Motion I - Chapter Chapter 2 Wave...

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