Accelerometers (was Sound waves)

[Phillip L Ford]

On Tue, 15 Jan 2002 19:44:46  
 John Delacour wrote:

>An accelerometer transduces variations in pressure to a voltage.  At 
>the point where the string meets the bridge (or where a tuning fork 
>meets the table)  particles of the bridge at that point are disturbed 
>and set in motion in the direction of the applied pressure.  How far 
>they move and how fast is not important at the moment, but at 
>nano-second zero they accelerate, leaving the remaining particles of 
>the bridge unaffected.  Exactly the same could be said of the 
>termination at the stud end of the string, except that the quantities 
>would be different; in both cases there is so some disturbance, which 
>certainly means movement, of particles at the meeting-point.
>
>JD
>
John,
I've broken my reply into two parts.  One is in response to this portion about
accelerometers.  The other is the response to the rest of your post about mechanics
of materials (I hope that description is accurate enough).
I think we may need to have a side discussion about accelerometers.  I'm not sure
I understand what you mean by saying an accelerometer tranduces variations in
pressure to a voltage.  Here's an excerpt from a previous post by Ric B:

Accelerometers measure acceleration, vibration, and shock. An accelerometer involves the mounting of a seismic mass attached to a damper
    and a spring inside a solid casing. The movement of the mass inside the casing is proportional to the force of acceleration on the device. Many
    accelerometers use either a capacitive or piezoelectric sensor to measure the position of the mass. Accelerometers are specified by the range,
    frequency response, and the sensitivity of the device. 

      -- Acceleration, vibration, and shock: 
         1. output units, mV/g 

I'm not an accelerometer designer, so I'm not really familiar with the details of their
operation.  But the description given here doesn't seem to involve pressure at all.
My understanding of the device is that it's intended to measure acceleration of the
point to which it is attached, not pressure, but perhaps I'm missing your point.

If I understand correctly what you are saying above then the accelerometer is only
indicating a local acceleration of some particles of the body, not an acceleration of
the body as a whole.
However, a bodily acceleration would also be registered by the accelerometer.  For
example:
1.  Let's say we have a tall, thin, flexible agraffe.  In my opinion, when the string is
vibrating, the agraffe will rock and roll (to use Robin's terms).  It will wave around
like a flagpole.  If an accelerometer is attached to the top of it it will register
acceleration.  Do you agree with this statement? (Note - I am not asking you to
agree that the agraffe moves, but to agree that if it did the accelerometer would
register an acceleration.)  If you do agree, then if we mount an accelerometer in
this way and see a positive reading, how do we know whether the agraffe is moving bodily
or some local particle in the agraffe to which the accelerometer is attached is
moving locally?

By the way.  I believe the agraffe could move in this way without the piano lifting off
the floor, the building in which it is located lifting off the ground, or the earth being
displaced from the solar system.  But I suppose that's another discussion.

2.  Let's say we have a very flexible capo.  Let's say it is very thin and short in cross
section and is only attached to the plate at the left end of the plate and the right end
of the plate.  It's not difficult for me to imagine that due to the vibration of a string the
capo would flex up and down.  (If we make the capo flexible enough it becomes essentially
a string itself which is being driven by the actual string.)  If an accelerometer were attached
to this capo I believe it would register an acceleration due to the transverse vibration or
flexure of the capo itself.  If we see a positive reading on this accelerometer how do we
distinguish that the reading is from this bodily movement of the capo rather than (or in
addition to) local movement of the spot to which the accelerometer is attached?

Phil F