Strings

A string has natural frequencys that it will vibrate at,  these are called harmonics.  Harmonics depend on tension, density, and length of the string.  Changing the length of the string, or changing a fret on a guitar, will change the sound the string produces.

The first three harmonics of a string are shown by the pictures below.  The wavelength of a string is the length of the black line from starting point, up, down, and back to the starting point, shown in the picture "2nd Harmonic."  The frequency is how many times one wavelength passes a certain point in a given time.  With these two quantities, you can calculate speed.  Speed is equal to the wavelength multiplied by the frequency.


Each string has its own natural frequency.  You can change the frequency of a guitar string by changing the fret (assuming the speed stays relatively the same).  Changing frets changes the length of the string since it cannot vibrate past the fret.  Waves with higher frequencies have a higher pitch than lower frequencies so as you work down the neck of the guitar the sound gets higher because the length is decreasing.

Background Image From: http://mccombs.nu/gallery/misc_guitar1/p1010002?full=1