[CAUT] coupled motion and other myths

[Richard Moody]

.....
Figures 3 and 4 
show the comparative decay rate for vertical vibration modes between one 
string vibrating alone and two strings vibrating together. The coupled 
string shows an initial peak followed by a steep drop and rise in 
amplitude (I think in another place in the 5 lectures it is claimed this 
is because of the antisymetric mode kicking in.. somebody may correct me 
if I am wrong here.).   The uncoupled string does not show this.

Maybe one the strings had a false beat in it?  He doesn't write about
talking to a piano technician in setting up his seeming elaborate laboratory
like observation of piano stings in vibration.  Yet some of his "readings"
might be due to a common phenomena known by technicians, but  not
necessarily by Science Phds.   It seems in these "studies" the piano tuner
is rarely mentioned, or if so, very offhandedly.  What other authority is
there in scientific experiments on pianos?  

OK, even if we all don't agree he knows exactly what is going on, the next
step is replication.  Can anyone demonstrate "coupled motion"   Aurally,
with tuning machines, only in a lab?    Rm




-----Original Message-----
From: caut-bounces at ptg.org [mailto:caut-bounces at ptg.org] On Behalf Of
Richard Brekne
Sent: Thursday, June 14, 2007 1:33 PM
To: caut at ptg.org
Subject: [CAUT] coupled motion and other myths

Hi Ric

The article is a bit longer then the one side in the link you have below 
of course... but this page is easy enough to explain I suppose.  
Basically he starts off by saying that two strings can either vibrate in 
phase or out of phase with each other. In the latter, which he refers to 
as the antisymmetric mode, the two strings vibrations will have a 
tendancy to cancel each other out... which causes the support (bridge in 
the case of the piano) to behave as if it was very stiff... unwilling to 
vibrate easily.  This otherwise known as a high imedance condition and 
results in a long sustain.. He notes that he is looking at the Vertical 
vibration of the string(s) only... for simplicity.

The rest of the page is pretty much experimental data that back up this 
opening statement.  The measurement you take issue below with... at 12 
seconds after the initial sound, is of course from a long string with a 
sustain time long enough to demonstrate the principle.  The amount of 
decay is going to be relative to the length of the string... so what it 
says about the first three seconds needs to be seen in terms of what 
percentage of the ring time the string has you want to know about. In 
the example string, three seconds is perhaps within the time frame that 
one sees the initial effect of the coupling take place. Figures 3 and 4 
show the comparitive decay rate for vertical vibration modes between one 
string vibrating alone and two strings vibrating together. The coupled 
string shows an initial peak followed by a steep drop and rise in 
amplitude (I think in another place in the 5 lectures it is claimed this 
is because of the antisymetric mode kicking in.. somebody may correct me 
if I am wrong here.).   The uncoupled string does not show this. The 
decay afterwards is at a higher amplitude for a longer period of time 
for the coupled string then the non coupled string.  Which is to be 
expected since the coupled string as stated initially forces the support 
to tend towards being stiffer... hence increasing acceptance impedance 
(resistance). Figures 5 and 6 show two strings vibrating (again only the 
vertical mode is being looked at here)