Del, No extra energy. Whatever the quantum of energy delivered to the system must be accounted for at all the various output stations, including heat, absorption, and radiation of sound. Clearly you already know this quite well, and have taught it for years. This subject is not easy to dice up in small, pat answers. There is no extra energy expended in a well hit ball verses a poorly hit ball. But two cases differ: the energy of the swung bat and incoming baseball can be identical in both cases. But batter A-Rod strikes the ball at the sweet spot on the bat sending the ball a long way, while batter B-Rod strikes the ball either too close to the hands (ouch, sting and small ball trajectory), and ditto for stroking the ball too far out on the bat. Inefficiency and wasted energy, but equal energy inputs in both cases. So, then, it is the force interface (with a complicated convergence of masses and velocities) that differs, and with concomitant effects. Analogies eventually fall flat and tend to obfuscate the real physics at hand. As I said (or at least suggested), my sense is that good piano tone does swell or bloom to one degree of another, some noticeably when the first attack and sustain mode begins to subside, and then again picks up as the impedance mode begins to shift. This later impedance model suggests (out of many possibilities) a less massive board wherein the initial attack/sustain mode is beginning to audibly die out, but then gets a second wind when the rotational vibratory mode of the string shifts out of its orthogonal bias. I have heard this, but the effect is not due to additional energy, but simply the way in a particular case that the energy and forces divide up and then manifest themselves. In a more balanced system, the bridging effect is more closely attached thereby exhibiting an ongoing "swell" if you wish; that is, no "second wind", just an ongoing wind (like many of my posts <G>). I suspect that this idea could easily devolve into mincing words and terms along with disparate aural experiences too difficult to put into words. Del, you may have not measured this so-called "bloom". Nor have I, but I can imagine that in a lab and with suitable EQ, this effect might be measured but, at the end of the day, the consensus would be more simply understood as either good tone, OK tone, or bad tone. Don't know if that more explains what I had said earlier. Gotta get back to work... Nick On Thu, Mar 17, 2011 at 10:12 AM, Delwin D Fandrich <del at fandrichpiano.com> wrote: > It's that "swelling of the tone" that I have a problem with. Your > explanation nicely accounts for the change in the rate of decay that pianos > exhibit following the initial chaotic attack but I fail to see where any > extra energy is coming from to "swell the tone." It is this "swelling" that > I have not seen measured. > -- Nick Gravagne, RPT AST Mechanical Engineering
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