i have no idea, but clear this up for me, is the string resonating on these frequencies? i think so, and if it is, the amplitud ought to diverge, am i right? i've thought about this for a while, for i needed to measure these frequencies on the lab and i wanted to know where to put the oscillator so it would all move as smooth as it could.
How is the force acting on the string? Is it a pulse?
If so the amplitude of the anti-node of the string is a function of the intensity displacement. In other words, if the string has a tension on it (some mass) and then you vibrate the string, the amplitude of the vibrator will determine the amplitude at the resonant frequency. In my experience that's around 60 Hz with a 20 Hz step bandwidth to the next resonant frequency.