"zero friction" bearings

[Ric Brekne]

Hi Stephen

Just musing but... it strikes me that the friction free bearing points 
are at the outset would preclude any kind of termination needed to 
connect the string to the bridge. The string would just vibrate against 
the wood of the bridge... buzzing like crazy for each downwards cycle.  
Also... since the initial part of the wave motion is more akin to a 
traveling wave the pulse traveling down the wave would just travel right 
through the area of the string that contacts the bridge.... nothing 
would be there to reflect it backwards... the same could be said of 
whatever contribution longitudinal wave motion in the string has. 

One other thought... when this traveling pulse hits the present bridge 
it doesnt seem likely  (to me) that the resultant motion introduced to 
the bridge is all that much in a direction perpendicular to the string 
plane.. i.e. "up and down". More likely it would seem to me that a 
strong force pulse along the string plane hitting the bridge would tend 
to want to move the bridge in the same plane.  Intuitively, we tend to 
think the bridge will resist any such sideways motion with great force 
because of the way its attached to the soundboard.... that would require 
the whole soundboard.. (and case) to start vibrating along the string 
plane. But we are dealing with extremely small distances here... and it 
strikes me that it is likely that this is exactly what happens during 
that first couple milliseconds. The transition the string goes through 
from this initial wave action to standing wave behavior is mirrored by a 
similar transition in the vibratory motion of the system (piano) as a 
whole.  At least my own sense of senseability brings me to think along 
these lines :)

Cheers
RicB



Stephen Birket writes:

Conversely you need some friction (aka pressure bar
bearing angle) to protect the speaking length from instability in the
front length, however it may originate. So add to my hypothetical
piano with friction-free bearings perfectly stable front (and back)
lengths as well.

To deflect one possible argument against, namely that the strings
would be unstable during hammer impacts, I would respond that: (a)
during the impact the string is not vibrating as a standing wave
anyway, so instability of tension is irrelevant,