Accelerometer (was Sound waves)

[John Delacour]

At 7:05 AM +0000 1/25/02, Phillip L Ford wrote:

>What I was asking is whether the point that the accelerometer is
>attached to has to be moving for the accelerometer to have a reading?  If
>the accelerometer is attached to the top of the bridge and the accelerometer
>is showing a reading then that point at the top of the bridge must be moving,
>regardless of what is happening to the molecules underneath it in the bridge
>or soundboard.  If that point was sitting fixed in space with the molecules
>beneath it doing whatever they are doing then the accelerometer would show
>no reading.  Do you agree with this?

That would depend on the type of accelerometer used and its g rating 
and frequency range.  There are all sorts and some would tell you 
nothing useful at all.

Besides, we have been dealing with the vibration initiated at the 
string termination in isolation and considering it in a plane normal 
to the soundboard.  There will also be transverse modal vibrations of 
the soundboard/bridge affecting the whole system and superimposed on 
the vibrations due to the flexure of the strings.  Owing to various 
factors the actual angle of the strings' flexures will be 
unpredictable and need to be factored in from separate measurements 
using who knows what devices.  In practice I'd say the whole test 
would be quite a challenge for any experienced lab technician.

I'm no expert in the use of accelerometers.  I've recently obtained 
two of them but have not yet devised experiments for putting them to 
use and am not sure how I'm going to set about it or whether the two 
units I've been supplied with are going to answer the questions I 
want the answers to.

We don't need any fancy devices or any doctorates of philosophy to 
investigate the phenomenon in question.  Here's a simple experiment 
anyone can carry out at no cost and which will provide evidence 
direct to the eye and ear.


RUBBER BRIDGE EXPERIMENT
________________________

On my string-making machine I stretch a No.23 wire (or a covered 
string) at a tension of about 80 lb.  The speaking length will be 
about 120 cm. and the frequency about 100 c/s, but anything will do.

About 120 cm from the end I set up my bridge/soundboard between the 
string and the machine bed.  Soundboard No. 1 is a whetstone and 
soundboard No. 2 is a cigar box.  My bridge is two rectangular 
india-rubber erasers one on top of each other (effectively one 
thickness) about 25 mm. high.  When I pluck the string, its 
transverse vibrations are clear to see and if my eyes were better, 
I'm sure I'd see movement at the string termination too.  Needless to 
say with soundboard No. 1 I hear very little sound.

Now I take my accelerometer, which is a straightish length of 2 mm. 
copper wire with a wooden bead at one end and a point at the other. 
(I also went out and bought a mechanic's stethoscope following 
Robin's suggestion, but this was actually less effective because of 
its stiffness and mass.  The copper wire, slightly bent, can follow 
the vibrations without damping them significantly)

Now I set the string vibrating and it sustains pretty well because 
the amount of energy being lost is not great.  I now hold the point 
of the wire to the rubber right next to the string termination and 
listen with the bead held against the little flap in front of the 
ear-hole, whose name I don't know.  The movement at the string 
termination is clearly felt as a vibration in the wire and the sound 
of the string is clearly heard complete with some quite high 
harmonics.

I then place the point of the wire on the whetstone directly below 
the string termination, and you'll not be surprised to hear I hear 
next to nothing.  Since the whetstone is rigid and immovable, no 
vibration is taking place.  I next move the point of the wire to 
positions on the rubber bridge further and further down from the 
string termination and as I do so, the amplitude of the sound 
diminishes and the higher partials disappear.  If I take soundings 
along the top of the bridge, the further I get from the string 
termination, the less vibration I get, not surprisingly.

Next I replace the whetstone with the cigar-box soundboard.  Now, of 
course I can hear the sound of the string radiating from the 
cigar-box.  I take the same aural measurements as before, and the 
vibrations at the termination are indistinguishable from those I 
heard when the soundboard was made of stone; but as I take soundings 
downwards through the bridge the amplitude falls off less steeply and 
the sound is not extinguished where the bridge meets the soundboard. 
However, I have lost quite a few upper harmonics.  These have been 
absorbed in the bridge, or damped, or "filtered out".  Indeed I have 
come across several references where the bridge is referred to as a 
mixer and a filter.  So the radiated sound that I hear contains the 
fundamental and a part of the harmonic spectrum, but not everything 
that was fed in at the top.

So, does the bridge move?  One thing I have surely to allow is that 
every particle between the string termination and the soundboard has 
moved before the soundboard is disturbed, and several more in the 
immediate vicinity, but each of them has moved a different amount and 
perhaps in different directions.  The more massive or the stiffer the 
soundboard, the less the particles near the bottom of the bridge will 
move in comparison with those near the top.  So long as there is some 
flexibility in the soundboard, every particle between it and the 
string end will move.

If anyone likes to regard this as bodily movement, they are free to 
do so, but I don't.  It is a localized disturbance of particles that 
tends to compress and to bend and this disturbance travels where it 
can and bounces back where it can't.  It's effect is to compress and 
to bend to varying degrees.

I have my flame-thrower ready for anyone that needs to inform me that 
piano bridges are not made of india-rubber, but I'll be happy to hear 
any serious criticisms of this experiment.

JD