false beats from ?? -...

[Robert Scott]

Ric Brekne writes:

> ..If we are to accept that a false beat is tied to the supposed variance
> in speaking length that the below math and reasoning tries to justify,then we must (and I mean imperativly must) expect a beat rate thatdiminsishes with the strings ability to deflect the pin as the strings

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.

> Further, the string already exerts considerable sidebearing pressure
> on the pin, and by the time the string starts oscillating in ellipticalpath it hasn't enough energy to overcome this side bearing one way or theother...

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.

> Thirdly, the initial pulse is 100 % vertical. The slight angle of thepin will deflect a very small portion of this in a purely sidewaysmotion... or to put it in other words, there is only a very small purelysideways component of the force exerted upon the pin by this initialenergy 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.

Of course there are other mechanisms for producing false beats.  Loose bridge pins is just one of them.

Robert Scott
Ypsilanti, Michigan