P&M Applets

Sound waves in air Wave on a String Standing waves Harmonic Sum

Fourier Series Loaded String Fourier Synthesis Game Anharmonics Amplification and Clipping

Applet Guidelines for “Harmonic Sums Applet”

Click here to launch the applet.

This applet, developed by the P&M Development Team, shows graphically the principal of Fourier superposition. The right side of the applet allows you to turn on and off the first three harmonics a string and control their intensity and whether they are highlighted or not.

When one of these resonant frequencies is turned on, a string to the left vibrating at this and only this resonant frequency is shown.

In class we learned that a string can vibrate at many of its resonant frequencies simultaneously. The string vibrating on the bottom left of the applet window represents what a string would like when it is vibrating at the harmonics that you have turned on above. You should be able to determine visually that this string is nothing more than the sum of the strings vibrating at single harmonics. Use the pitch/tension slider, and the highlighting to change the speed of vibration to help with the visualization.