impedance for 99

[Jory A. Olson]

I promised I would be good and not post unless I had something really important to say.  That time has come....

I must say that I find this discussion soundboard impedance to be fascinating.  As an electrical engineer I'm comfortable with the idea of soundboard impedance.  I even think it wouldn't be that hard to measure mechanical impedance.  If voltage is analogous to force and current is analogous to velocity (not of the wave but of the displacement from the force) if should be possible to mount a linear motor (like the motor from a speaker) to the soundboard and measure the displacement with a laser interferometer.  The first time derivative of displacement is velocity.  One could then calculate both the real and imaginary parts of the impedance by "doing the math".  It's ohms law for soundboards!  That would be something like:  Force/Velocity = Impedance  The tricky part would be getting the timing of the force and the measurement of the displacement to be synchronous.  I'd be shocked if one of those HP Fourier Analysis thingy's the gearheads (mechanical engineers) are always using for vibration analysis couldn't be used to make this measurement.  Doesn't sound tough to me, but wadda I know, I'm just a sparky (electrical engineer).  We leave the greasy stuff to the gearheads :)  Thoughts?

On another, but related note, I keep hearing piano technicians try to draw analogies between soundboards and speakers.  Most recently Ron did this when he wrote:  

"In use, a soundboard assembly is a driven diaphragm, sort of like a speaker cone, that has to accommodate and respond to frequencies ranging from roughly 27Hz-4200Hz. That's woofer, tweeter, and crossover, all in one unit. Let's see the audio engineers do that in a high performance speaker!"
I'm not trying to pick on Ron, I'm sure he know exactly what he's talking about or he wouldn't have used the phrase "...sort of like...".  In actual fact an audio transducer (speaker to the rest of us) is nothing like a soundboard.  A speaker uses a linear motor to drive a cone shaped of stiff paper, appropriately enough called a cone, in a pistonic fashion.  The resulting sound is highly direction and frequency dependent.  Higher frequencies are more directional.  Lower frequencies are less directional.  Two people sitting in the same room, one on axis and the other off axis, can have completely different impressions of the sound quality because they are in fact hearing different things.  Additionally, any normal sized speaker behaves as a point source of sound.  That is, the sound amplitude falls of as the inverse-square of the distance.  If you're twice as far away the sound is one-fourth as loud.
A soundboard, on the other hand, is driven with a bending wave initiated by the bridge.  The bending wave travels to the rim and is reflected back.  Different modal patterns appear on the soundboard at different frequencies.  Doug Richards could probably make some pretty cool Finite Element Analysis animations of the soundboard in motion, given enough time and "free" computer time.  Anyway, the sound from a soundboard is not nearly as directional as from a speaker.  Likewise, the sound does not fall off as the inverse-square of the distance because the piano soundboard is not a point source.
These are just two of the differences between a speaker and a piano soundboard.  There are others mostly having to do with what happens to the speaker cone at higher frequencies.
Anyway, I don't think a speaker and a piano have much in common.
There is a new speaker technology being pushed by a company called NXT that uses a carbon-fiber panel much like a soundboard.  A transducer initiates a bending wave on the carbon-fiber panel.  The exact point of excitation is very important.  FEA is used to find the right point of excitation.  I've only heard small (4 x 6") models, but the sound is much better.  I think you will be seeing flat stereo speakers in the near future, based on the same acoustics as the piano soundboard.  This is the woofer, tweeter, and crossover all in one that Ron was asking for!  You can see a set of these new speakers by going to http://www.cc-inc.com/home.asp and searching for item number 38830.  A company called Benwin is making a set of PC speakers using NXT technology.  They're $129.95 (USD).
Jory