## Illustration 17.5: Resonant Behavior on a String

Thus far we have considered either a traveling wave or a traveling pulse. The wave traveled off to infinity unencumbered by any barrier. Here we consider a pulse on two strings, but the strings are pulsed multiple times. To complicate matters the two pulse frequencies are different. Run the animation and consider the results (position is given in meters and time is given in seconds). Restart.

How can we understand what is happening? First we notice that the pulse is reflected at the wall. Second we notice the effect of good and bad timing. Which animation has the good timing and which one the bad timing?

In the bottom animation the timing is awful! The waves add up in a way that does not yield a maximum wave amplitude. All we get is a jumbled-up mess.

The top animation shows the effect of good timing. All of the pulses add constructively to the returning reflected wave to give the largest wave amplitude possible. Whenever we get successive contributions to the wave adding in this way, we call it a resonance. It is like pushing a swing. If you push a swing at just the right frequency (good timing), large amplitude motion will result. If you apply the same force, but at a different frequency (bad timing), not a lot usually happens. In order to get a large amplitude you must push at the same frequency as the natural frequency of the swing.

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.