When a string with fixed ends vibrates (e.g. plucking a guitar string) Fourier Theorem says that the vibration can be expressed as a sum of its normal modes, which are sinusoidal vibrations with frequencies that are all integer multiples of the fundamental frequency.
My question is really simple: since the resulting vibration is a sum of a large number of simple vibrations, with what frequency is the string really vibrating (since, after all, it is a vibration)? Are all the points in the string vibrating with the same frequency but with amplitude modulated in space as happens with the normal modes?
I'm not asking which pitch do we perceive (the fundamental frequency), but at what frequency is the string vibrating.