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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

wave
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