AW: Sound waves(The behavior of soundboards)

[Tim]

-----Ursprüngliche Nachricht-----
Von: owner-pianotech@ptg.org [mailto:owner-pianotech@ptg.org]Im Auftrag
von Ron Nossaman
Gesendet: Montag, 7. Januar 2002 23:51
An: pianotech@ptg.org
Betreff: Re: Sound waves(The behavior of soundboards)


Robin,
Salmon aside, there are still the two fundamental problems I have with this
explanation that I've had from the beginning. The first is string supplied
compression waves going through the bridge without displacing it in space
(physically moving it), and the second is these waves somehow turning the
corner and becoming longitudinal waves in the soundboard which, upon
reflection from the rim, meet themselves coming and transform into
transverse waves, which then move the bridge. There are, of course,
compression waves happening in the bridges and soundboard assembly, but I
have a little more straightforward concept of what does what. Give this an
honest read and see what you think.

The problem with the idea of a compression wave not moving the bridge is
that the driving frequency cycle must be high enough that at least one
complete cycle is completed while the wave started at the beginning of the
cycle is still in the bridge.

In it's simplest form, assume a string vibrating at it's fundamental at 440
CPS, and a bridge 1.5" tall. Call a string cycle 360° starting (for
visualization) at 3:00 on a clock face and progressing to 90° at 6:00, 180°
at 9:00, 270° at 12:00, etc. So 0+-180- would be putting positive pressure
on the bridge, and 180+ - 360- would be applying negative pressure. The
speed of sound cross grain in hard maple is about 35,000"/second. One cycle
at 440cps takes 0.0022727+ seconds. The compression wave travels from
bridge top to bottom in 0.000042857+ seconds. Arbitrarily, benchmark from
+0° with the string moving downward.

At +0°, positive pressure change is being applied to the bridge. Surface
molecules are compressed closer together and compression wave starts in
bridge, moving down. Actually moving everywhere but up, so the net
direction is down.

At 6.79° into the string cycle, the compression wave reaches bottom of
bridge. Meanwhile, pressure at the top of the bridge has steadily
increased, so there is no rarification pulse behind the pressure wave to
allow the bridge molecules to return to their original positions. At this
point, at the precise moment that the leading edge of the compression wave
passes from the bridge into the soundboard material, the bridge molecules
>from the string to the soundboard have *all* been moved down. Not half up
and half down in compression and rarification where they will average no
net bridge displacement, but *all* down at once. That means the bridge has
moved before the soundboard has, and the string was what moved it, not the
soundboard. This also means that the bridge has not only moved, but it is
now *moving*, and is *accelerating* because there is still pressure on top,
and unrelieved compression in the bridge. In fact, the *acceleration rate*
is *increasing* because the pressure on the bridge top is still mounting
faster than it is being relieved on the bottom. This is still at under 7°
of the 180° "compression " phase of the 360° string cycle. The bridge will
continue to move downward until at some point between 180°+ and 360°- in
the string cycle, the negative pressure will overcome the momentum by the
reverse of the process that built it up on the pressure side of the cycle,
and the bridge will follow along faithfully behind the string movements.
Note that, as that quote I posted from the "Vibration Theory and
Applications" book, the bridge movement will lag behind the string
movement, and will be of lower amplitude than the string movement because
the string will have to overcome the system inertia and drive the system at
a frequency higher than it's resonant frequency.

Once the bridge is put in motion by the string, the soundboard, by virtue
of being attached to the bridge, goes with it very much like the string
does when it is struck and moved by the hammer, except that the board is
pushed by a gradually applied load rather than struck by the bridge. A
local transverse deformation of the assembly results because the forced
movement can't overcome the inertia of the system all at once. The local
deformation then propagates outward as a progressive transverse wave as the
transverse deformation and stiffness of the material overcomes the inertia
in the section of the assembly in it's path. The propagation rate is
dependant on the stiffness and mass of the material, so it won't progress
at the same rate in all directions. These progressive transverse waves, or
traveling waves, will then reflect from the rim, back on themselves, and
form the interference patterns of standing waves displacing air at cyclic
frequencies similar to the driving frequency of the string, and forming the
compression waves we hear as sound.


That's essentially it. The strings move the bridge, the bridge moves the
soundboard, the soundboard moves the bridge, the bridge moves all the
strings, and it cycles until all the energy absorbing parts, whether they
contribute to the sound or not, disperse the energy. Beyond the action of
physically displacing the bridge by carrying the  surface displacement from
the top to the bottom of the bridge and back, and carrying the results from
the assembly to our ears in the air, I don't think longitudinal or
compression waves have much to do with soundboard action.

Ron N