Sound waves(The behavior of soundboards)

[John Delacour]

At 11:41 PM +0000 1/10/02, Phillip L Ford wrote:
>On Thu, 10 Jan 2002 12:01:59 
>  Ron Nossaman wrote:
>>
>>http://www-ccrma.stanford.edu/~jos/waveguide/Dynamic_Terminations.html
>>
>>
>  >When a traveling wave reflects from the bridge of a real stringed 
>instrument, the bridge moves, transmitting sound energy into the 
>instrument body. How far the bridge moves is determined by the 
>driving-point impedance of the bridge, denoted . The driving point 
>impedance is the ratio of Laplace transform of the force on the 
>bridge to the velocity of motion that results.

This is not at all at odds with previous statements I have made, 
which I repeat below, since I see that Ron N. is still trying to 
pretend that I have denied mobility in the system.  For good measure, 
I'll take an extract first:

_____

"IF THE SYSTEM WAS COMPLETELY UNYIELDING AT THE BRIDGE, THERE WOULD 
BE TOTAL REFLEXION AND NO ENERGY TRANSFER" -- JD (see below)
_____

This all has to do with impedance, and that has not so far become the 
topic of the discussion, and in my view, recently expressed, ought 
not to be considered at this stage but later, when the matter of the 
sound waves has been dealt with more thoroughly.  It is not any 
bodily movement of the soundboard that is responsible for the 
radiation of the string's sound into the air.  We can later set about 
discovering the effects of impedance, and at that point there will be 
a gradual fusion of the two  related notions -- that of sound 
propagation and that of the impedance required for this to happen in 
the desired fashion.

At 12:29 PM +0000 12/26/01, John Delacour wrote:
>As the system is stiffened up (I am deliberately using language that 
>I hope is generally understandable) so stress or pressure increases 
>at the point where the string meets the bridge.  The pressure 
>increases and the movement decreases.  It is the ratio between these 
>two quantities that constitutes "acoustic impedance" and any 
>movement of the bridge/soundboard system plays no part in the 
>propagation of the sound except in so far as it creates the 
>necessary environment for that propagation to take place.  The sound 
>is propagated through the bridge and the soundboard in the same way 
>as sound is always propagated and the bodily movement of things is 
>not involved.

At 10:39 AM +0000 1/5/02, John Delacour wrote:
>The flexibility and mass of the system is concerned with its 
>acoustic impedance, just as in a piano.  It is not "up and down 
>motion" of the plate that radiates the sound any more than it is in 
>the piano.

At 10:01 AM +0000 1/6/02, John Delacour wrote:
>a) sound (=vibrations, = mechanical energy) is propagated through 
>the system as waves of pressure in the media.  These are all 
>longitudinal waves that radiate from the source, which is the point 
>at which the string meets the bridge.  I will say a little more 
>about this in a moment, because a previous topic might lead to 
>confusion on 'longitudinal waves'
>
>b) IN ORDER for this propagation, or transfer of energy, to take 
>place, there must be a regulated degree of mobility (flexibility, 
>lack of rigidity) in the system at the point of transfer, namely at 
>the string termination.  Contrast the termination at the stud, where 
>minimum mobility and maximum reflexion of the transverse wave of the 
>string is required.  The required degree of mobility will vary from 
>instrument to instrument (eg. violin v. piano) and also from place 
>to place within each instrument.
>
>If the system was completely unyielding at the bridge, there would 
>be total reflexion and no energy transfer, the only audible sound 
>being that set up my the pressure waves set up in the air by the 
>string's movements.



PF:
>I interpret this to mean that the bridge and top are moving in direct response
>to the input from the string.

That's a pretty ambiguous statement.  The bridge and top are 
obviously moving because the string has caused them to move, but they 
are _moving_ at a frequency that is not related to the frequency of 
the sound generated by the string.  It is not this movement that is 
responsible for the acoustic radiation that reaches our ears.  How 
many times do I have to draw this distinction?!

JD