waves1 - Physics 53 Wave Motion 1 It's just a job Grass...

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Unformatted text preview: Physics 53 Wave Motion 1 It's just a job. Grass grows, waves pound the sand, I beat people up. — Muhammad Ali Overview To transport energy, momentum or angular momentum from one place to another, one can give these mechanical properties to an object and send it to the destination. This is how they are transferred from a gun to a target by means of a bullet. But there is an indirect way. Microscopic particles of the source can interact with nearby particles, transferring energy, etc., to them. These particles in turn can transfer these quantities to their next neighbors, and so on down the line until the destination is reached. This kind of step-wise transmission is called wave motion . The particles occupying the intervening space and which pass along the energy, etc., constitute the medium for the transmission. These particles move back and forth only a little distance from their original positions, while the “disturbance” travels from the source to the receiver, which might be a very large distance. There are two distinct types of wave motion: Longitudinal waves . The particles in the medium move back and forth along the line traveled by the energy. Sound is an example of this kind of wave. Transverse waves . The particle motion is perpendicular to the line along which the energy moves. Waves on a stretched string is an example. So are electromagnetic waves, but in that case there is no intervening medium of particles, only the Felds. Waves can be a combination of these types. In water waves, for example, the particles move around in circles. General description Waves in a string provide a useful example for analysis, because one can actually see the motion of the medium. PHY 53 1 Wave Motion 1 We consider a string stretched between two points on the x-axis, and subjected to a disturbance that displaces some of the particles in the y-direction. At t = 0 let the shape of the string be a curve given by the formula y = f ( x ) . Because of the interaction between neighboring particles, the disturbance will be passed along the string. We will assume (as an approximation) that the shape of the disturbance does not change while it moves down the string. If the disturbance moves in the + x direction with speed v , then at time t the new shape of the string will be described by y = f ( x − vt ) , where f is the same function as before. Mathematically, it is just like moving the coordinate origin to the right by the amount vt . The situation is as shown. If the disturbance moves in the – x direction with the same speed, the new formula will be y = f ( x + vt ) . This is an important property of the functions describing waves: if the variables appear in the form x − vt then the wave moves in the + x-direction; if the form is x + vt the wave moves in the – x-direction....
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This note was uploaded on 10/19/2011 for the course PHYSICS 53L taught by Professor Mueller during the Spring '07 term at Duke.

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waves1 - Physics 53 Wave Motion 1 It's just a job Grass...

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