String instruments create sound via
vibrations. If you were to simply pluck a string or play a harmonic,
the string will vibrate at its fundamental frequency.
fundamental frequency = (wave velocity)/2L
wave velocity = sqrt (tension/(m/L))
m = string mass, T = string tension, L = string length
hyperphysics.phy-astr.gsu.edu
f1 = fundamental frequency.
When you press down on a string that's vibrating, the frequency changes
since the length decreases. If you add vibrato to a vibrating string,
the wave velocity will change depending on the rate of your vibrato.
Below is a link to a clip about a cellist that looks into the ideal
sound wave rate for cello vibrato.
pbs.org