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In the figure below is
shown an elastic string that is being driven by a rotating bar to produce
a sinusoidal oscillation. The string is modeled by massive beads connected
by massless (and invisible) springs. The wave produced moves to the right
and out through the window for a long distance. It is shown at a time *t* =
0. Use the *x-y* coordinate system shown by the dotted lines and the distance
scale shown by the rulers.

A. The rod driving the wave goes through a single up-down-up cycle in a time
of 0.2 seconds. Write an equation for the displacement of the bead at position
*x* at time *t*, *y*(*x,t*). Explain briefly why you chose the representation you did.
If you use symbols (other than *y*,* x*, and *t*) rather than numbers in your equation,
explicitly give their numerical values.

B. With what speed will the wave travel down the string? Explain.

C. If the rod is slowed down so that it goes through a cycle in a time of 0.4 seconds, what will happen to the appearance of the wave? After it has been doing this for a few seconds, sketch a graph of what a snapshot of the wave will look like.

Page last modified February 10, 2011: O55