impedance and empericism

[Delwin D Fandrich]

----- Original Message -----
From: Richard Moody <remoody@midstatesd.net>
To: <pianotech@ptg.org>
Sent: June 14, 2000 10:36 PM
Subject: impedance and empericism


> OK numbers to the nearest whole place then.
> As the son of an electrical engineer, I have always wondered what concept
> "impedance" was supposed to convey when used as "soundboard impedance".
He
> tried his best to show me how electrical impedance was measured and used
in
> formulas. So you can see why I have always been expecting formulas for
sound
> board impedance.   So not even knowing what the concept is, How can I
think
> of a better term.

The concept of mechanical impedance is covered in many references and texts
dealing with moving mechanical things.  One fairly common reference is the
Shock & Vibration Handbook edited by Cyril M Harris (mine is the third
edition).

What we are mostly concerned with is 'driving point impedance,' that is, the
ratio of the driving force -- the vibrating string -- acting against a
system having resistance (damping), spring and mass.  The basic relationship
is Z (impedance) equals F (the exciting force) divided by v (the resulting
velocity).  From there it gets very complex since impedance is both
frequency variable and phase dependent.



>       There is that school of science that says in effect, if it can't be
> measured, you don't know what you are talking about.   I think they really
> say if it can't be measured it can't be defined, which is the same as
> existance for them.  This I think came out of the arguments for and
against
> the concept of "the ether", the hypothetical medium for electromatic
> radiation like air is for sound.

Actually, soundboard impedance is also fairly easy to measure.

All it takes is some expensive equipment.  A signal source (usually a
tunable oscillator feeding an amplitude controlled amplifier) is used to
drive a shaker (something like a loudspeaker motor without the speaker cone)
that is configured to drive the soundboard (usually at some point along one
of the bridges) through an impedance head consisting of a force transducer
and an accelerometer.

A signal of some frequency and amplitude is fed to the shaker which supplies
vibrating energy through the impedance head to the bridge forcing some
resulting movement in the soundboard/bridge system.  The amount of force
required to move the bridge is measured by the force transducer and the
resulting bridge/soundboard acceleration and velocity (the velocity signal
is integrated from the acceleration signal) is measured by the
accelerometer.  From this we can determine the mechanical impedance of the
bridge/soundboard system.  (Also, by comparing the force signal with the
velocity signal we can determine the impedance phase angle.)  We now know
the mechanical impedance for that specific driving level and frequency at
that specific spot on the soundboard/bridge system.  Since impedance is a
complex function if any of these parameters are changed the impedance also
changes.  By sweeping the signal frequency through the piano's typical
frequency band we can map the impedance for that driving point on the
bridge.

So, while soundboard impedance is relatively easy to measure, it remains
extremely difficult to calculate and predict.  If reliable methods exist to
calculate soundboard impedance, I don't know of them.

Regards,

Del
Delwin D Fandrich
Piano Designer & Builder
Hoquiam, Washington  USA
E.mail:  pianobuilders@olynet.com
Web Site:  http://pianobuilders.olynet.com/