Hi rkc908,
I'm afraid I don't quite understand your question. Are you asking about the vibration of guitar strings? Or are you asking about the vibration of molecular bonds, which is a very different question. I'll assume you are talking about vibrating guitar strings, but please correct me if I'm wrong.
The length of a guitar string controls the wavelengths at which the string can vibrate because nodes must exist at the two ends of the string. The background section of the Project Idea has information about this, as well as an equation you can use to calculate the frequency of the harmonics of the string. Since the standing wave
must a node at each end of the string, if a particular frequency of sound (which we hear as pitch) doesn't have a wavelength that allows there to be a node at each end of the string, then the string in question will not be able to produce that pitch because it cannot resonate with that frequency.
When the Project Idea asks about modes, it is talking about vibrational modes or harmonic overtones. The background section to the Don't You Fret project idea has some additional background information:
https://www.sciencebuddies.org/science- ... p009.shtml
Be sure to also take a look at the links in the bibliographies of both Project Ideas.
Other objects have resonant frequencies, although the allowed modes are much more complicated than one a vibrating string.
If this doesn't answer your question, please post back with some additional details so that I can better help you.