Interference and Diffraction HW 4

Interference and Diffraction HW 4 - MasteringPhysics...

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[ Print View ] Physics 228 Spring 2008 Interference and Diffraction (Ch. 35, 36) Due at 11:59pm on Monday, February 18, 2008 In part G, assume that the wave that is reflected does not pick up a phase shift Pi. In Part H, assume that the wave that is reflected does pick up a phase shift of Pi. View Grading Details A Simple Introduction to Interference 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 At time , what will be the displacement at point ? Express your answer in meters, to two significant figures. ANSWER: = 0 Page 1 of 11 MasteringPhysics: Assignment Print View 5/7/2008 http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1116515
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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 B Choose the picture that most closely represents what the rope will actually look like at time . ANSWER: A B C D Part C 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 . Page 2 of 11 MasteringPhysics: Assignment Print View 5/7/2008 http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1116515
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The phase for a plane wave is a somewhat complicated expression that depends on both position and time. For most interference problems, you will work at a specific time and with coherent light sources, so that only geometric considerations are relevant. Consider two light rays propagating from point A to point B in the figure, which are apart. One ray follows a straight path, and the other travels at a angle to that path and then reflects off a plane surface to point B. Both rays have wavelength . ANSWER:
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Interference and Diffraction HW 4 - MasteringPhysics...

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