In your physics lab, an oscillator is attached to one end

Chapter 15, Problem 15.75

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In your physics lab, an oscillator is attached to one end of a horizontal string. The other end of the string passes over a frictionless pulley. You suspend a mass M from the free end of the string, producing tension Mg in the string. The oscillator produces transverse waves of frequency f on the string. You dont vary this frequency during the experiment, but you try strings with three different linear mass densities m. You also keep a fixed distance between the end of the string where the oscillator is attached and the point where the string is in contact with the pulleys rim. To produce standing waves on the string, you vary M; then you measure the node-to-node distance d for each standingwave pattern and obtain the following data: String A A B B C M 1g,cm2 0.0260 0.0260 0.0374 0.0374 0.0482 M 1g2 559 249 365 207 262 d 1cm2 48.1 31.9 32.0 24.2 23.8 (a) Explain why you obtain only certain values of d. (b) Graph md2 1in kg # m2 versus M 1in kg2. Explain why the data plotted this way should fall close to a straight line. (c) Use the slope of the best straight-line fit to the data to determine the frequency f of the waves produced on the string by the oscillator. Take g = 9.80 m>s 2 . (d) For string A (m = 0.0260 g>cm), what value of M (in grams) would be required to produce a standing wave with a node-to-node distance of 24.0 cm? Use the value of f that you calculated in part (c).