Sound waves(The behavior of soundboards)

[John Delacour]

At 2:00 PM -0800 12/15/01, Robin Hufford wrote:

>Excursion of the bridge and soundboard at this point is neglible if 
>extant at all.  One could, I suppose, call this a ripple but this is 
>misleading and of little significance.
>      I agree with J. Delacour that a compression wave passes through the board
>:  this is a stress wave which has, of course, an  attendant strain.  The
>strain itself is the displacement but this displacement is on an atomic and
>molecular level as the particles oscillate about their neutral 
>position.  There
>is no excursion or flexing of the soundboard at this point as the forces
>involved are not sufficient to actually move the board, a point which anyone
>observing weights placed upon, go bars used,  or even people sitting on
>soundboards while under repair in shops might begin to suspect.

When I walked away from this topic, having proposed such a test and 
had it arbitrarily dismissed, in my own mind I had hardly travelled 
beyond the point at which the string meets the bridge, though others 
were anxious to generalize and get by any means to talk of the 
rippling soundboard.  I can't myself make such a leap of faith, so I 
would like to return to this meeting-point.

The excitation of the string by the hammer or plectrum sets up 
vibrations that eventually reach our ear as a musical sound through 
the medium of the air.  Of that I think there is no discussion.

For the vibrations of the string to reach our ear, they must disperse 
themselves through elastic media which, in the case of the 
traditional piano, comprise primarily steel or brass (the bridge 
pin), beech, maple, mahogany, box (the bridge), hard glue, spruce and 
whatever the rim is made of (if the rim is considered, as later it 
might be, but let that pass).  So far, in my mind, there is no room 
for discussion.

At my starting point, one end of the vibrating string is held firm by 
downward pressure (the "down-draft") and lateral pressure (the 
"side-draft") in the acute angle formed by a steel or brass pin 
driven into a length of maple or laminations of maple or beech with 
mahogany or ash and capped with maple, beech or box.  It is required 
that this junction of the end of the string with the bridge be solid.

At the same time, the whole bridge is subject to the downward 
pressure of the other strings and is in equilibrium between this and 
the upward force of the soundboard.  In the case notably of 
Grotrian-Steinweg, the bridge itself is very broad and is stiffened 
on the reverse of the board by a substantial "counter-bridge". 
Experience shows that no reasonable increase in the height of bridges 
(and consequent exponential stiffening) will lead to negative tonal 
effects, but rather the reverse.  The effective bridge, therefore, of 
our most illustrious predecessors, seems to be by design a pretty 
rigid affair and might be made even more rigid to good effect.

Interlude: The long bridge of the piano I've been working on today 
(which I consider an excellent piano) is made of two lengths of solid 
maple spliced at the middle.  In the treble section it is 
increasingly canted to about 25 degrees at note 88 and is capped with 
box.  The remainder is capped with quartered beech.  The total height 
of the bridge is 32 mm. and its width 27 mm.  This design grew out of 
68 years of experience during which nearly 20000 pianos had been made 
by this firm.  End of interlude.

I can now apply the point of a vibrating tuning fork to the bridge 
and its sound will become more audible.  Whether I apply the fork to 
the top of the bridge or the side of the bridge, the quality and 
audibility of the sound will be essentially the same, though 
differences in grain direction and wood type may cause slight 
variations.

The vibrations cause by the transverse movements of the taut string 
are passed into the bridge at a point equivalent to the point of the 
tuning fork pressed against the bridge, and this point in both cases 
is static and not mobile.  From this point the vibration, or 
molecular disturbance, radiates into the elastic medium that is the 
beech or box or maple + the steel of the pin and travels as 
compression waves in all directions as fast as the medium, the grain 
direction etc. allow.  Virtually every molecule of the wood or steel 
will be displaced and oscillate in response to the kicks and shoves 
from its neigbours.  It is the oscillation of the molecules next to 
the glue line, excited by kicks and shoves from all directions within 
the bridge, that will now raise a rumpus in the soundboard.  The 
bridge so far remains unmoved, its internal tranquility severely 
disturbed but outwardly unmoved, unrippled, unfurrowed.

Serious comments only please.

JD