Solution: 4245 concern a vibrating guitar string. Snapshotsof the guitar string at

Chapter 12, Problem 44

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4245 concern a vibrating guitar string. Snapshotsof the guitar string at millisecond intervals are in Figure 12.95.The guitar string is stretched tight along the x-axis from x = 0to x = . Each point on the string has an x-value, 0 x .As the string vibrates, each point on the string moves back andforth on either side of the x-axis. Let y = f(x, t) be the displacementat time t of the point on the string located x unitsfrom the left end. A possible formula isy = f(x, t) = cos t sin x, 0 x , t in milliseconds. (a) Sketch graphs of y versus x for fixed t values, t = 0,/4, /2, 3/4, .(b) Use your graphs to explain why this function couldrepresent a vibrating guitar string.

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