CONTEXT-RICH A commonly used physics experiment that

Chapter , Problem 65

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CONTEXT-RICH A commonly used physics experiment that examines resonances of transverse waves on a string is shown in Figure 16-34. A weight is attached to the end of a string draped over a pulley; the other end of the string is attached to a mechanical oscillator that moves up and down at a frequency that remains fixed throughout the demonstration. The length between the oscillator and the pulley is fixed, and the tension is equal to the gravitational force on the weight. For certain values of the tension, the string resonates. Assume the string does not stretch or shrink as the tension is varied. You are in charge of setting up this apparatus for a lecture demonstration. (a) Explain why only certain discrete values of the tension result in standing waves on the string. (b) Do you need to increase or decrease the tension to produce a standing wave with an additional antinode? Explain. (c) Prove your reasoning in Part (b) by showing that the values for the tension F for the nth standing-wave mode are given by and thus the is inversely proportional to (d) For your particular setup to fit onto the lecture table, you chose and Calculate how much tension is needed to produce each of the first three modes (standing waves) of the string.