Illustration 17.6: Plucking a String

n: 1 2 3 4 5 6 7 8

Please wait for the animation to completely load.

A green string of length L = 28 cm (position is given in centimeters) is shown plucked to x = 6 cm and y = 3 cm. The unstretched position of the string is shown in gray. Changing the slider changes this plucking point along the length of the string in the x direction (the y point of the pluck remains the same). You may also look at the Fourier components that make up the green stretched string by clicking on an n value. The relative size of these sine waves is depicted by the graph on the right. Restart.

We have thus far looked at using a Fourier series to describe an arbitrary periodic wave (see Illustration 16.5 and Illustration 16.6). For the plucked string, we must consider a different way to add up waves to get the Fourier series. Here we must consider any wave that is zero at the ends of the string (since the plucked string, like a standing wave, has ends that are tied down). Therefore, we find that our plucked string can be described in terms of a Fourier series as

f(x) = σ An sin (n*π*x/L),

where in the animation L = 28 cm (see Illustration 16.5 and Illustration 16.6 for more details on the periodic case).

When you get a good-looking graph, right-click on it to clone the graph and resize it for a better view.

Illustration authored by Morten Brydensholt, Wolfgang Christian, and Mario Belloni.
Script authored by Morten Brydensholt, Wolfgang Christian, and Mario Belloni.
© 2004 by Prentice-Hall, Inc. A Pearson Company
HTML updated for JavaScript by Aidan Edmondson.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.