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When you flip a coin, you hear a ringing sound. I know that the source of the sound is the thumbnail hitting the coin, but it seems to be filtered by the spinning of the coin. Specifically, the faster the coin spins, the smoother the tone and it seems the spectrum becomes more uniform.

So my question is, physically, what is the exact phenomenon that is causing the filtering? It seems to be some form of frequency modulation (or amplitude modulation? I suspect it's the former but I could be wrong).

my other question is, what are the exact characteristics of this filter? I know that the filter will be a function of the angular frequency of the coin, which I'll call $\omega_m$, but other than that I don't know where to start on how to characterize it.

rurouniwallace
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I think a simpler explanation than some kind of sound filtering as a result of the speed of rotation is that when you hit the coin with more force (resulting in a faster speed of rotation), it increases the amplitude of the coin's vibrations, enabling higher modes of vibration, and thus changing the spectrum. I'm skeptical about your claim that the spectrum is more uniform unless you've done a spectral analysis of the sound. It's difficult to draw specific relations between the timbre of a sound and the specific qualities of the sound's spectrum, but generally a "mellow" sound is one with a lower amount of high overtones relative to its low ones, whereas brighter, more piercing, or grittier sounds have a higher amount of the high overtones. When I flip my coin, I hear a fairly bright sound, so I would predict more of the high overtones.

I'd expect the coin would vibrate in modes similar but not identical to those pictured on this Wikipedia page.

Another note is that if you did a spectrum analysis on the coin's sound, it would be non-harmonic e.g the important frequencies in the spectrum would be non-integer multiples of the lowest frequency. This is a property of most percussion instruments, because their different modes of vibration don't vibrate in integer multiples of the lowest overtone.

I hope I've answered the question sufficiently.

David
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