Homework for Standing Waves

Standing Waves in a rope:

Download from the class website the Excel sheet that has the results of the standing wave experiment we did in class.

(a) Tabulate the raw data (# nodes, frequency, wavelength, for several standing waves) and also do the necessary conversions (explain, please!) to plot the “dispersion relation” (ω vs. k) for the rope and obtain the phase velocity of the waves in the rope from the graph.

(b) Explain how the application of Newton’s 2nd law to the system predicts a value for the velocity in terms of the physical parameters of the vibrating string system. Measure those parameters to predict the phase velocity and compare with the result from (a).

(c) Why are the waves you observed not traveling?

(d) What is the significance of a linear dispersion relation? Give an example of a system where the dispersion is not linear.

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