Duplex

[Ron Nossaman]

>Without realizing your hope, Ron, I'd like to consider a case that 
>allows less rein to the imagination.
>
>Suppose we have a 3" speaking length terminated at the front by a 
>perfectly massive over-bar under which the string passes at an angle 
>of about 15° to continue for 1" up to a duplex bridge and then 
>onwards over the bearing felt to the wrestpin.
>
>I pluck the 1" front length (which itself has no musical qualities) 
>and the 3" speaking length responds with a faint note at its own 
>frequency.

Hi JD,
Yes it does, and it will do it anywhere in the piano regardless of the
length of that         segment, or for that matter, the bearing angle. The
plucked segment oscillates transversely, just like any reasonably well
terminated plucked segment, but the terminations between segments aren't
clamped, they are pivots. The transverse excursion of the plucked segment,
minute though it may be, levers against the terminating pivot and, because
of the stiffness of the wire, levers the segment on the other side of the
lever (the speaking length) into transverse movement as well. The now
oscillating speaking length will naturally sound at's own vibrational
frequency. The same thing happened across the counter bearing to the tuning
pin segment as well, only you can't hear it as readily as the speaking
segment. The stiffness to mass ratio of the short segment is considerably
higher than that of the speaking length, so the speaking length will sound
longer after the plucked segment has dumped to much of it's initial energy
to adjacent segments to maintain a high enough excursion amplitude to be
audible. Unless, that is, the  bearing angle is shallow and it's length is
a close fraction of the speaking length. In your example, with a 10°
bearing angle or less, the duplex would quite possibly continue to sound
audibly. That's how tuned front duplexes work. I posted to the list a
couple of years ago about just this effect. I thought is was really
interesting when I stumbled upon it. Still do.  


Ron N