Sound waves(The behavior of soundboards)

[John Delacour]

At 6:13 PM +0000 1/15/02, Phillip L Ford wrote:

>However, a body cannot have sustained acceleration without moving. 
>And a body cannot have velocity without being in motion.  This is 
>what I call playing with semantics.  Del has said that tests showed 
>that an accelerometer mounted to an agraffe or a capo registered 
>acceleration.  This means motion to me.  And this would seem to be 
>inconsistent with the position that the ends of the string don't 
>move.  So, a reasonable response would be an explanation of why this 
>really is consistent (if it is) with the position that the ends of 
>the string don't move.  To say that an accelerometer measures 
>acceleration and not motion is a smoke screen to avoid explaining a 
>seeming inconsistency.

I beg you not to accuse _me_ of putting up smoke screens.  I have no 
interest at all in winning an argument but want to get at the facts. 
As to semantics, I have been most careful in my choice of terminology 
and expressions.

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.

This disturbance initiates a wave of pressure that passes through the 
medium at a certain speed, namely the 'acoustic velocity' of the 
medium or the 'speed of sound' in that medium, which I believe I'm 
correct in thinking are synonymous expressions.

If we consider our body, the bridge, as a single vertical "ray" or 
line of particles rather than a three-dimensional mass of particles, 
it will be easier to explain.  The particles of an elastic body have 
a certain relationship to each other in space when they are in 
equilibrium.  If a homogeneous elastic body is heated, for example, 
the body, as we all know, will expand and the particles be more 
distant from each other.  The bond, i.e. the atomic force, between 
them becomes weaker.  At a certain temperature, the bond will become 
so weak that the body liquefies, and at a higher temperature this 
fluid will vaporize.  In the cases we are considering, we are forcing 
the particles of the body to take up different positions in relation 
to each other.  We are opposing a force or pressure to the forces 
that holds them in equilibrium.  So long as we don't overdo it, much 
of the energy we have expended in stretching the wire or compressing 
the bridge, or whatever, will remain as strain energy in the body, 
and this will be converted to kinetic energy, when our force is 
removed, to restore the body to its original shape.  All this is to 
emphasize that any elastic body, by definition, is composed of 
particles that can to a degree (that being the elastic limit of the 
material) be moved closer together or further apart by an imposed 
force.

To return to our bridge consisting of a vertical "ray" of particles 
and let me return to an analogy I used earlier -- that of a 
transparent tube containing a stack of little cylindrical magnets 
disposed North<>South<>S<>N<>N<>S<>S<>N etc.  Let the magnets 
represent particles of an elastic medium and the repulsive force 
between them the atomic forces between them.  This ray of magnets is, 
of course, compressible.  If we close the bottom of the tube so that 
the bottom magnet can't move, and press down on the top magnet, we 
oppose our force to the magnetic force and the magnets are pressed 
closer together.  If we move the top magnet a certain distance and 
maintain the pressure, the magnets will (very fast but 
_not_instantaneously_) take up different positions in respect to each 
other.  Each magnet, or particle will have been displaced a different 
amount and the ray will be in a state of compression.

I'll break off there and continue the analogy once you have accepted 
that this is a clear description of a demonstrable experiment.  If 
there are any problems with it, I'll try to make myself clearer in 
response to your queries.  So far, of course, I have attempted only 
to draw a picture of a one-dimensional bridge, which will take us 
quite a long way and is easy to visualize.

JD