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 “Loaded String Applet”

Click here to launch the applet.

Much like the "Harmonic Sums applet" the loaded string applet allows you to visualize a string vibrating at the harmonics that you specify. In the case below, the 1st and 3rd harmonics have been turned on:

The difference here is that in addition to being able to set the harmonics and see what the string looks like, you can also do the opposite. That is, you can drag the string into an arbitrary position and see what harmonics would be necessarily be involved in order to place the string in the position.

Change the "Display Phases" to "Display Modes" or "Display Left + Right." Displaying the modes will show you how each of the Fourier components are vibrating to make up the wave. Displaying Left + Right displays the left moving wave along the string with the right moving wave (remember that a standing wave always consists of a left and right moving wave summed together). Displaying phases shows you where each of the harmonics is in its cycle (we don't concern ourselve with phases in this course)

To modify the string you simply drag it with the mouse. By default this plucks the string, but you can also use the pull down menu to shape the string arbitrarily.

Plucking the string simulates the shape the a string would be in when it is plucked on a stringed instrument (a guitar, for example). Check the “Sound” box to hear what a guitar string would sound like when plucked in various ways. Notice that the reason it sounds difference is due to the different harmonics make up the wave. If you could pluck a guitar exactly in the shape of a sine wave what does this applet imply that it would sound like? Would it sound more like a flute or a guitar?