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 don't vary this frequency during the experiment, but you try
strings with three different linear mass densities \(\mu\). 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 pulley's 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:
(a) Explain why you obtain only certain values of \(d\). (b) Graph \(\mu d^2\) (in
kg \(\cdot\) m) versus \(M\) (in kg). 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 \(g = 9.80 \, \mathrm{m/s}^2\). (d) For string A (\(\mu =
0.0260\) 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).
