When I was in college, we had to do a couple of experiments in Physics lab class to study string vibrations.
Frequency, nodes, etc.
When a guitar string is pressed against a fret and that string is plucked, it sets off a pretty complex set of vibrations.
Since they are not plucked in the exact center of each string, guitar strings vibrate both at the fundamental note's frequency and also there are a whole host of harmonic vibrations at frequencies mathematically related to the frequency of the fundamental note.
The physical construction of the guitar influences the vibrations of the strings in response to the string's vibrations making the various pieces of the guitar vibrate. Even a solid body electric guitar can have it's tone greatly enhanced by being crafted of as few solid pieces of good wood as possible, and these tone woods will impart some harmonic influence back to the strings and out through the amplifier.
This is why guitars can be SO EXPENSIVE. The highest quality, large pieces of tone woods are as expensive to buy as they are resonant and beautiful to look at.
Yeah, there are a lot of cheap guitars in the world, and a surprising number of them sound good and play good too, but when a guitar is constructed from high quality pieces of properly dried woods, this wood can impart back to the strings even richer harmonic content resulting in a great sounding guitar whose tone is thick with harmonic content that is pleasing to the human ear.
For me this following very short video is mind blowing. I love this kind of stuff.
Although I knew the principles of string vibrations, I've never seen them in real-time action.
This video was simply shot with a camera with a high speed shutter, so that when the video is watched at the normal speed of the song, you can hear AND see the dramatic ways in which the strings vibrate.
Notice that the fingering and plucking of the strings are in time to the sound of the music. Although it almost looks like slow motion, it's not.
I wish we had been shown a video similar to this in Physics lab, studying string vibrations would have made a lot more sense, a picture (video) painting a thousand words and all that.