User Note: We talked about frets on a guitar and how when you push the string into the fret board it raises the pitch on the note by changing the length of the standing wave on the string. Another interesting thing you can do is this: after plucking the open string, just lightly touch the string with your finger at the 12th fret. A sound like a bell or flute will result, as you create the second harmonic of the original standing wave. Here's what happens: by touching the string lightly while it's vibrating, you cause it to come to rest at that point you're touching. This results in another node, as shown above with the second harmonic. Touching the string at the 7th or 5th fret can make the third and fourth harmonics, with higher numbers of nodes. But if you touch the string someplace that does not result in equal segments between nodes, no harmonic is produced and the string stops. This is simply math. Guitar players can tell you all the spots where harmonics can be produced, even if they don't care too much about the math and physics behind it. (Some of them care though!)
