Imagine that you have plucked a string and it is vibrating as a standing wave at its fundamental tone (frequency f1). You leave it there and later on come back with the intention of bringing it up to the second tone (frequency f2). What should you do? It seems obvious: apply a stimulous oscilating at such second frequency (f2). But what happens then with the energy of the first vibration oscilating at f1? Is it necessarily wasted? Is there no way to benefit from such energy? Can't you build on the existing vibration and apply a stimulous of frequency (f2 - f1)? For example, if I arrive with my arm vibrating at (f2 - f1) and then grasp the string that was already vibrating at f1, will it somehow be raised to vibration level f2?