Here’s a lesson on harmonics by justinguitar.com. The Clear Science staff thinks this is pretty good and clear.
If you like heavy metal (and who doesn’t?), here’s Dimebag Darrell giving a physics lesson on harmonics.
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!)
Since we were talking about guitars and how their pickups work, the Clear Science staff wanted to point out that all kinds of physics can be illustrated with a guitar. Take for example the vibration of the strings, which produces the notes. The strings are held stationary two places: at the nut, shown by the blue line, and at the bridge, shown by the grey line.
When you pluck a string, you set up a standing wave, with stationary nodes at the nut and bridge. When you fret the string (i.e. push it down with your finger), you change the distance between these nodes, and it changes the note.
The 12th fret is exactly halfway along the string, and when fretted there will produce a note one octave higher than the unfretted string. (For example, the top string is generally an E, and the note at the 12th fret is a higher E.) The 7th fret is 2/3 of the way along the string, and the 5th fret is 3/4. These special frets are usually marked with pearling or with some dots.
So we wondered, since sound travels through gases, does that mean you could hear a sound in a nebula? It will have to do with pressure. Pressure is the force per unit area exerted on any object due to the surroundings. Atmospheric pressure on Earth is about 101.3 kPa (kilo-pascals), but it varies up and down a bit depending on the weather.
Absence of pressure is called a vacuum. Outer space is pretty close to a vacuum, being about 0.1 pico-pascals, which is close to zero. Since sound is a wave of pressure, there is a threshold minimum pressure wave humans can hear, and it is about 20 micro-pascals. To hear sound, the surrounding pressure would need to be higher than that, to support a wave of that amplitude.
Wikipedia has a very nice list of significant pressure values, which the list above is partially compiled from.
