I mean, what it's saying it just that the energy decays exponentially. The energy loss is proportional to the energy.
That's a testable hypothesis.
Pluck a string, record the sound. See how the amplitude decays. If the hypothesis is correct, then it should be exponential in time. When displayed on a decibel scale, which is logarithmic, it will be a straight line.
Well, at least that would be true assuming that the energy loss is proportional to the radiated sound power, which seems like a decent assumption to me.
Hey, why don't you check the web?
Maybe someone's done the experiment it already?
That formula hasn't fallen from the sky after all!
I'm a bit mystified about why the guitar mass—I'm assuming that's what the M stands for—is inversely proportional to energy loss.
Are you telling me, if I encase it in massive block of cement, it barely makes any sound but vibrates for ages?
Is that a thing? Do heavy guitars "ring" longer?
Although it seems strange, it again is a testable hypothesis. Get a heavy and a light guitar and see if they ring longer/shorter.
However, weight differences might be marginal and these constants K in the equations may be different between guitars, making the whole experiment ...
Not very insightful.
Theory-wise this formula is hardly a stroke of genius. To me, it just seems like semi-random first guess/simple model.
"Lots of things are exponential or power laws; let's see if this is exponential"
If it fits the data we'll, that's great!