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 cent (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 y(x, 1) y, (x, t) y (x, t) where n(x, t) Csino,tsinkx (x, t) Csino,tsinkx

Question: 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

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.

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

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