© Daniel Kleppner.
Waves such as these can be observed on a guitar string using a stroboscopic light that flashes at the rate of vibration and makes them look still. The amplitudes in the drawing are much larger than one would find on a stringed instrument, but the patterns are identical. The wave pattern marked "n = 1" would generate the fundamental tone of the string. The wave marked "n = 2" would then generate the octave. The geometrical relationship between musical tone and the length of a string was discovered by the Greek philosopher Pythagoras, who considered the knowledge sacred and closely guarded the secret. (Unit: 5)