midterm1 - Spring 2010 PH 113 Midterm Exam No 1 Answer both...

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Spring, 2010 PH 113: Midterm Exam No. 1 Answer both problems. Each problem is worth 50 points. Only fully derived and explained solutions will receive full credit. A final answer with no derivation or justification, even if correct, will not receive credit. Problem 1. Mechanical waves in a string . A uniform string of total mass M and length L is suspended vertically in a gravitational field with acceleration of free fall g . The coordinate y measures the height of an element of the string from the bottom (so that the endpoint of the string at which it is suspended is at y = L , and the lower endpoint is at y = 0 ). a) Make an argument based on dimensional analysis for the speed of waves in the string. Hints : Remember, it is the local parameters that determine the speed. Do not assume the string is homogeneous, as the weight along the string that is balanced by the string tension depends on the height! b) Find the wave speed by first finding the tension and linear mass density. Compare your result with the one you have found above in a). Are they equal or not? If yes,
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