Mastering Physics 4

Mastering Physics 4 - Course PHYSICS260 Assignment 4 Due at...

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Course PHYSICS260 Assignment 4 Due at 11:00pm on Wednesday, February 27, 2008 A Simple Introduction to Interference Description: Interference is discussed for pulses on strings and then for sinusoidal waves. Learning Goal: To understand the basic principles underlying interference. One of the most important properties of waves is the principle of superposition . The principle of superposition for waves states that when two waves occupy the same point, their effect on the medium adds algebraically. So, if two waves would individually have the effect "+1" on a specific point in the medium, then when they are both at that point the effect on the medium is "+2." If a third wave with effect "-2" happens also to be at that point, then the total effect on the medium is zero. This idea of waves adding their effects, or canceling each other's effects, is the source of interference . First, consider two wave pulses on a string, approaching each other. Assume that each moves with speed meter per second. The figure shows the string at time . The effect of each wave pulse on the string (which is the medium for these wave pulses) is to displace it up or down. The pulses have the same shape, except for their orientation. Assume that each pulse displaces the string a maximum of meters, and that the scale on the x axis is in meters. Part A
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At time , what will be the displacement at point ? Express your answer in meters, to two significant figures. ANSWER: = Part B Choose the picture that most closely represents what the rope will actually look like at time . ANSWER: A B C D The same process of superposition is at work when we talk about continuous waves instead of wave pulses. Consider a sinusoidal wave as in the figure. Part C
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How far to the left would the original sinusoidal wave have to be shifted to give a wave that would completely cancel the original? The variable in the picture denotes the wavelength of the wave. Express your answer in terms of . ANSWER: = Part D In talking about interference, particularly with light, you will most likely speak in terms of phase differences, as well as wavelength differences. In the mathematical description of a sine wave, the phase corresponds to the argument of the sine function. For example, in the function , the value of at a particular point is the phase of the wave at that point. Recall that in radians a full cycle (or a full circle) corresponds to radians. How many radians would the shift of half a wavelength from the previous part correspond to? Express your answer in terms of . ANSWER: phase difference = radians Part E The phase difference of radians that you found in the previous part provides a criterion for destructive interference. What phase difference corresponds to completely constructive interference (i.e., the original wave and the shifted wave coincide at all points)?
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This homework help was uploaded on 04/09/2008 for the course PHYS 260 taught by Professor Chen during the Spring '08 term at Maryland.

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Mastering Physics 4 - Course PHYSICS260 Assignment 4 Due at...

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