Plucking the Guitars


When one is asked about the steady state motion of the string , what does this mean. I realize that I can describe the motion of a wave by superpositions of wave trains going right plus trains going left. And thus, Fourier representation of these two wave trains lead us to y(x, t) = A sin(wt) sin(kx). But if there is a force acting on the string besides the tension force, what do they mean with steady state of the string?

Thank you,


In general steady state motion is motion that is periodic so that we can predict that in the future there will be motion that will be the same as that in the past. When you pluck a guitar string, for example, you pull the string into two straight line segments about the location of the pick. Then when the string is released, the Fourier components of the wave initially are those contained in that bent line waveform. The high frequency components lose energy faster than the fundamental waveform so they die out over time, leaving the string vibrating in its fundamental mode. In this example we would call the fundamental mode the steady state motion of the string since it persists farther into the future than did the transient higher frequency components.

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