Combining Standing Waves. A guitar string of length L is plucked in such a way that the total wave produced is the sum of the fundamental and the second harmonic. That is, the standing wave is given by

With w1= uk1 and W2 = vk2€¢
(a) At what values of x are the nodes of y1?
(b) At what values of x are the nodes of y2?
(c) Graph the total wave at t = 0, t =1/8f1 t = 1/4.f1, t = 3/8f1and t = 1/2f1.
(d) Does the sum of the two standing waves y1 and y2 produce a standing wave? Explain.

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y(x, 1) = y, (x, t) + y.(x, t) where n(x, t) = Csino,tsinkx »(x, t) = Csino,tsinkx