Ric Brekne writes: / Robert Scott writes:/ /Instead of thinking about speaking length, you could also look at a vibrating string as a spring/mass resonant system. The resonant frequency of such a system is determined by the mass of the vibrating member (the string) and the spring constant of the spring that is acting to return the mass to its central position. If we can model the loose bridge pin (and the wood that is holding it) as a spring, then its springiness adds to the springiness due to string tension. This causes a slight decrease in the spring constant, which is the ratio of restoring force to deflection distance. Therefore the pitch is different when the bridge pin is loose. / Again, if this is the case, then one has to expect that there are practically no exceptions to the rule. The fact is that a very significant number of loose bridge pins do not result in any false beat. The fact remains also that one can find this same exact kind of false beat evident in very tight pins. When there are so many exceptions evident then its usual to start looking in another direction for an explanation. Not to mention beat rate occurrences that dont match up to the theoretical beat rates the hypothesis yields. If something doenst add up... then well... it doesnt. > Further, the string already exerts considerable side bearing pressure > on the pin, and by the time the string starts oscillating in elliptical path it hasn't enough energy to overcome this side bearing one way or the other... /That all depends if the loose pin is behaving like a spring. You can pre-load a spring with a large force and it will give a certain amount. Then if a small amount of additional load is applied, the spring will give a slight amount more - in strict proportionality. However, if you can establish that a loose pin is not behaving like a spring, then you would be right./ It strikes me that you need to show the pin IS acting like a spring. You have basically supposition and conjecture at this point. There is no hard science to confirm either way to begin with, and as I have pointed out a few times now, the significant number of times the occurrence (or not) of false beats that do not adhere to the loose pin hypothesis to begin with forces (at least me) to question its validity. > Thirdly, the initial pulse is 100 % vertical. The slight angle of the pin will deflect a very small portion of this in a purely sideways motion... or to put it in other words, there is only a very small purely side ways component of the force exerted upon the pin by this initial energy of the string. /Precession of the direction of vibration happens even when the termination points are nearly perfect. What Peter Weinbreck (sp?) showed in his articles in the 1970s in Scientific American was that the initial vertical motion of the string corresponded to the higher rate of decay as the vertical motion energy was carried away into the bridge and soundboard. Then, as the string precessed into a more elliptical pattern, the horizontal component of the vibration encountered a much more rigid bridge than the bridge as seen by the vertical component. For this reason the energy in the horizontal component of the vibration did not decay as quickly. This can be directly observable by plotting the loudness as a function of time and noting that sound decays quickly at first, and then more slowly afterwards. / Why, yes... but I dont see how that addresses the point I made. Namely that the side bearing by the string on the pin is already too great for the vibration of the string in either stage of its vibration to overcome. Further if there was any chance of that, the variant amount of side ways force on the pin that must occur between the initial horizontal phase of string vibration and the elliptical phase of vibration during decay would dictate variances in the false beat that are not in keeping with what we actually observe. The hypothesis dictates variance but observation yields constancy. /Of course there are other mechanisms for producing false beats. Loose bridge pins is just one of them. / At this point I remain skeptical to the latter. And it certainly isnt a shown fact. Not by a long shot. But hey... should be easy enough to measure any such presumed sideways motion and see if it then matches theoretical beat rates that should occur. But like I said, I would be surprised at this point if any such measurements would do anything else then refute the whole idea. Cheers RicB Robert Scott Ypsilanti, Michigan
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