Sound waves(The behavior of soundboards)

[John Delacour]

At 12:36 PM -0600 1/31/02, Ron Nossaman wrote:

RH
>>There is no need to posit any kind of physical, substantial motion 
>>to account for the bouncing of the fork.  In fact, such an idea is 
>>thoroughly erroneous.   The reflection from the end of the fork 
>>causes the stress wave which is, in fact, what we are talking about 
>>here, to demonstrate itself as a kind o displacement of the end. 
>>This is strain and does not require the fork to be moving to occur. 
>>Such an idea is at odds with every analysis of this subject.
>
>And which analyses are these? Where might I find every one of these
>analyses of the details of handle movement in a tuning fork ruling out mass
>reaction?.................

I'd like to know where you get _your_ notion of bodily movement of 
the shank of the fork, what brand of "geometry and mathematics" leads 
you to your conclusions and how Newton has misled you.

Here is what two eminent acousticians in direct descent from Newton 
have to say on the question:

"A tuning fork can be considered to be two vibrating bars, both 
clamped at their lower ends" [Morse IV. 15]

Here is Rayleigh's rationale of the tuning fork:

"[With one clamped bar] in consequence of the oscillation of the 
centre of inertia, there is a constant tendency towards the 
communication of motion to the supports, to resist which adequately 
the latter must be very firm and massive.  In order to obviate this 
inconvenience two precisely similar springs and loads may be mounted 
on the same framework in a symmetrical manner.  If the two loads 
perform vibrations of equal amplitude in such a manner that the 
motions are always opposite...the centre of inertia of the whole 
system remains at rest and there is no tendency to set the framework 
into vibration. ... In fact any part of the motion which does not 
conform to the condition of leaving the centre of inertia unmoved is 
soon extinguished by damping." [Theory of Sound I.56]

 From this immobile centre of inertia will radiate periodic 
compressions of the particles.  If the shank of the fork is held 
loose, a small amount of this energy will be transmitted into the 
fluid of the fingers but most of it will be reflected internally. 
Particles all round the surface of the shank will be "dancing" in and 
out with minuscule amplitude of oscillation but with great force, so 
that unless the fork is held firmly in contact with the resonant 
system (e.g. the table) the momentum of these molecules will be 
sufficient to push the whole fork away.  This is not because the fork 
is moving up and down (or sideways) but because the particles at the 
surface are oscillating.  It makes very little difference to the 
amplitude of the transmitted sound whether you press the fork 
vertically against the table or flank-wise parallel to the table.

JD