Plucking the Guitars
Question:
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,
Answer:
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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