Sounds produced when sections of a string vibrate separately are called?

Answer 1

harmonics.

When the string vibrates as a whole, it is vibrating in a mode called the fundamental, and sounds the lowest pitch that the open string can make. If you touch lightly on the string at a location that marks an even division of the string, such as the half-way point, or 1/4, 3/4 or 1/5, 2/5, 3/5, 4/5 point, you will cause the string to vibrate in sections, and a higher pitch will sound, determined by the length of the vibrating sections. Additionally, because physics is the way it is, all the sections of the string will vibrate, with points of non-motion forming between the sections. These are called nodes. If you touch the middle of one of these nodes, you will silence the entire string!

The pitches of vibration are related to the length of the vibrating parts, as I said before. If you divide the string into integer fractions, 1/1 (the whole string), 1/2, 1/3, 1/4, 1/4, etc. you will produce the pitches corresponding to the overtones or harmonics of the string. This relates to Fourier's theory, which says that a complex tone can be decomposed into a combination of harmonically-related components. The pitches, if the fundamental 1/1 is accepted as the Unison (the interval formed when two notes that are exactly the same are played together), form the following intervals:
1/1 (whole string): unison (also known as the fundamental
1/2 (half string): octave above the fundamental
1/3 (third string): octave plus a perfect fifth* above the fundamental
1/4 (etc.): two octaves above the fundamental
1/5: two octaves and a pure third* above the fundamental
1/6: two octaves and a perfect fifth above the fundamental
1/7: two octaves and a flatted seventh above the fundamental
and so on.

*The harmonic pure third is not the third found on the piano. For reasons I won't go into here (look up 'temperament' and 'equal temperament' on wikipedia), the piano's third is made sharper and the fifth is flatter than the pure (and perfect) intervals. This is done so that the size of each semitone is an equal ratio. The study of scales, intervals, and temperaments is an entire subject of its own!)

A long-known principle is resonance. If two violins are set side-by-side and tuned exactly together, and a string is bowed on one of them, the same pitched string on the other will vibrate. The sound from the first violin travels through the air to the body of the second violin (as it does to your ear) and vibrates it. When the body vibrates, the string of the same pitch also is vibrated, and because it is just exactly tuned to that pitch, it begins to resonate with the vibrations, and will continue to vibrate, even if the first string is silenced.

This principle allows us to analyze the component tones of complex sounds: Helmholtz, a German scientist, made glass bubbles with a drawn part to fit into his ear and a large opening at the other end, and he tuned the size of the bubbles so the air inside resonated with certain tones. He was able to hear the components at that frequency of complex tones that came from violins and Guitars using these bubbles if the instruments played notes that contained that frequency component, but could not hear them if the instruments played tones that didn't contain that frequency. This is how the theory of decomposition into component tones was verified.

Harmonics provide us stringed instrument players with a good mechanism for tuning: if two strings are pitched a perfect fifth apart, you can find the 1/3 part of the lower (which sounds an octave and a fifth above that open string) and compare it to the 1/2 point of the upper (which sounds two octaves above that open string.) Since the harmonics produced this way fall on the same note, tuning the strings until those harmonics lose their beat ensures that the strings are tuned exactly a perfect fifth apart!