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Phy 232
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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QUESTT
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A string defines the x axis, with the origin at the left end of the string. The string has tension 19 Newtons and mass per unit length is 14 grams / meter. The left-hand end of the string is displaced perpendicular to the string in a cyclical manner in order to create a traveling wave in the string. At clock time t the position of the left-hand end of a long string is y = .54 cm * sin ( ( 9 `pi rad/s) t ). What equation describes the displacement a point 16.7 meters down the string as a function of clock time? If the position of the left-hand side is x = 0, what is the equation for the displacement as a function of clock time at arbitrary position x? University Physics: Show that your equation satisfies the wave equation. What is the equation for the shape of the string at clock time t = .042 sec? This question is giving me some trouble. I know how to answer the first part of the question, but am unsure about the other three.
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This is completely equivalent to one of the Introductory Problem Set problems. Locate that problem and its solution. If you have questions about specific aspects of the given solution, I'm glad to clarify.
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Also, I am having trouble with this problem.
Show that the function y(x,t) = .8 sin( 650 t - .77 x ) satisfies the wave equation, and give the equation of motion for the point at x = 1.931.
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Regarding the wave equation, that is the equation that relates y_xx to y_tt. This is a very easy problem using partial derivatives.
Find the speed of the pulse (this is related to the preceding exercise, in which the speed of the pulse is simply related to the coefficients of x and t within the sine function.
Then find y_xx and y_tt.
One of the ratios, y_xx / y_tt or its inverse, is equal to the square of the pulse speed.
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