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OSU PHYSICS 1251 - 10 Prob 11

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3/26/2014 Master Ithttp://www.webassign.net/v4cgi/questions/tutorial_popup.tpl 1/2Master ItA student holds a tuning fork oscillating at 258 Hz. He walks toward a wall at a constant speed of 1.25 m/s.(a) What beat frequency does he observe between the tuning fork and its echo?(b) How fast must he walk away from the wall to observe a beat frequency of 4.80 Hz?Part 1 of 4  ConceptualizeAn electronic burglar detector detects beats between the broadcasted signal and the Dopplershifted reflectionfrom a moving surface. The method used in the experiment described here is similar. The student hearsbeats at a rate he controls through his walking speed. We assume the speed of sound to be 343 m/s.Part 2 of 4  CategorizeWe must consider a double Doppler shift, one shift for the wave reaching the wall from the moving tuningfork, and another shift for the wave reaching the moving observer.Part 3 of 4  AnalyzeThe student moves toward the wall such that vs = +vstudent and v0 = 0. The wall acts as a stationary source,reflecting the wave with a frequency given byAs the student moves toward the source of the reflected sound (the wall), we have that vs = 0 andv0 = +vstudent. In this case, the frequency is given byand substituting the expression we found above for f', we have the following.(a) When the student walks toward the wall f'' is larger than f, so the beat frequency isf ' =f =f .v + v0v − vsv v − vstudentf '' = f ' = f ' ,v + v0v − vsv + vstudentv f '' = f = f v v − vstudentv + vstudentv v + vstudentv − vstudent3/26/2014 Master Ithttp://www.webassign.net/v4cgi/questions/tutorial_popup.tpl 2/2Substituting the given values and the speed of sound into this equation, we havefor the beat frequency.Part 4 of 4  Analyze(b) When the student is moving away from the wall, the sign of vstudent changes and f '' is smaller than f. Inthis case, we haveSolving for vstudent and substituting the given values, we have that the speed of the student walking awayfrom the wall must bein order to observe the given beat frequency.FinalizeIndoors, reflections from other walls may complicate these observations. Changing beat frequency bychanging motion can be observed in many situations. For example, children whooping while they play onswings in a playground outside a building with a large, high, flat vertical wall will hear the beat frequencyincrease in the reverberating echoes the higher they swing.fb =f '' − f = f − f =f − 1 = f .v + vstudentv − vstudentv + vstudentv − vstudent2vstudentv − vstudentfb = 258 Hz = 1.89 Hz2 1.25 m/s343 − 1.25 m/sfb =f '' − f = f − f =f 1 − = f .v − vstudentv + vstudentv − vstudentv + vstudent2vstudentv + vstudentvstudent = = = 3.22 m/sfbv2f − fb 4.8 Hz 343 m/s2 258 Hz − 4.8


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OSU PHYSICS 1251 - 10 Prob 11

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