Very cool! Also: might not absolute amplitude (volume) give away a lot of mass information relative to a control mass? "The bigger they are, the louder they fall" kinda deal?
Didn't they account for that? "Since the energy of a coin, if it's falling from a fixed height, is proportional to its mass, I would expect the sound energy to be proportional to its mass as well. So, this is what I did. I integrated the power spectral densities and fit them to a linear relationship with respect to the mass. I obtained:"
There's a fun Numberphile episode just about this topic. https://www.youtube.com/watch?v=MfzNJE4CK_s
By far, it is my favorite trick for impressing dining company.