Violin bridges

[John Delacour]

At 7:51 AM +0000 1/6/02, Phillip L Ford wrote:

>I looked at your reference John. By the way, who is Mr. Parr? I 
>don't see anything in there that contradicts what I said about the 
>bridge motion.

I don't know who he is, but I found the article interesting and serious.

No, it would not necessarily contradict what you said, but I think 
you are still missing the point.  That is not surprising in view of 
the amount of noise there has been in these discussions, especially 
the repeated imputation to me of the denial of movement in the 
system, which I have had repeatedly to refute.

Robin's latest post (Message-ID: <3C38073E.1D24C6@airmail.net> is 
worth reading first, since it gives some more useful stuff, but the 
point I have been at pains to get across throughout is that

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.

c)  The mobility of the system has no effect on the nature of the 
transfer of energy, but only on the flow of energy.  Other factors, 
such as the internal stucture of the media, will also affect the flow 
but we need not be concerned with these at the moment.  An analogy is 
sometimes drawn with the flow of electrical energy, and  acoustic 
'impedance' is a term borrowed from the electrical sciences.  If the 
terminals of an accumulator are connected with a thin wire, there 
will be a considerable resistance to the current (flow) of 
electricity; if by a copper bar, very little resistance and thus 
great current.  The nature of the current and the means of its travel 
is, however, the same in both cases.  The effect is different.  In 
the piano we are looking for a certain effect -- we neither wish it 
to get red hot nor to explode!  We require certain ratios of sound 
pressure to flow in order to achieve the proper development of the 
'sound'.

__

On longitudinal waves:  In the topic "compression Waves" and related 
threads, we talked a bit about longitudinal waves in the piano string 
and were here dealing specifically with the _resonant_ frequencies of 
stretched wires in the longitudinal mode.  This is a special case and 
not really at issue here, any more than the resonant frequencies of 
the soundboard are at issue at the moment.  When children stretch a 
wire between two cocoa tins and create a toy telephone, the voice of 
the children is propagated as logitudinal pressure waves along the 
wire, and this is the way sound is always proagated; however in this 
case, and in most cases, we are not concerned with the natural 
frequency of that wire vibrating in longitudinal mode.  This, as well 
as the resonant frequencies of a soundboard system, do crop up as 
issues -- as they did for Conklin -- but this is another matter.

>   It does say something about the time of travel of the vibrations 
>in the bridge and vibrations 'circling around the incision'  which 
>seems to be at odds with what I see in some of my references.  Here 
>are a couple:
>
>http://hyperphysics.phy-astr.gsu.edu/hbase/music/violin.html#c5
>
>An excerpt therefrom:
>
>The action of the violin bridge is essential to the tone of the 
>instrument. It's shape and function have been developed over 
>centuries. Underneath the treble side of the bridge (where the E 
>string rests) is the sound post which extends from the front to the 
>back plate of the instrument. Since this side of the bridge rests on 
>this post, it is essentially fixed and acts as a pivot for the 
>rocking motion of the remainder of the bridge. It does however, 
>couple the sound energy from the top plate to the back plate of the 
>instrument.

Yes, I see no argument here.  Almost the same could be said of the 
piano.  Del's mention recently of a "hinged soundboard" might be 
considered somewhat analogous and I have here a pinao from 1880 which 
does have a hinged, or rather cantilevered soundboard.  All the many 
devices that exist to regulate, localize, restrict the flexibility or 
mobility of the system have nothing to do with the _nature_ of the 
energy transfer.

>Underneath the bass side of the bridge (where the G string rests), a 
>long, thin wooden strip called the bass bar is attached, almost 
>parallel to the strings. This bass foot of the bridge is more free 
>to move, and its motion is the point of transfer of energy from the 
>strings to the top plate of the instrument.

Note well the use of words here!

This whole topic is, a Richard has said, very interesting, and there 
is a lot to be learned.  I have already learned a fair amount and 
only wish my knowledge of mathematics were deeper in order to aid the 
learning process.  I have tried in my postings not to fly too many 
kites and to work step by step.  Robin's latest post brings us back 
to the essential starting point, which is the termination of the 
string at the bridge, where the transfer of energy begins, where the 
inital stress is set up.  I want to get a clear idea of what happens 
here.  At the moment I see a molecular disturbance occurring here 
which radiates into the bridge; and I use the word 'radiate' in a 
strict sense, in that the pressure waves travel outwards from the 
source as the rays of the sun or the spokes of a wheel from the hub. 
These waves travel just as much along the bridge as down through it, 
though not necessarily with exactly the same speed or amplitude, 
since various factors will modify these.  Before we even get to the 
soundboard, there is plenty to consider.

I am frankly not interested in the Nossaman theory of sound:

At 10:48 PM -0600 12/5/01, Ron Nossaman wrote:
>My problem with the use of the word "sound" here was the impression that
>the soundboard works with internal compression waves. While sound that we
>hear by atmospheric transmission is a pressure wave propagation, the
>pressure wave propagation isn't the primary driver of soundboards.

It strikes me he really has a big problem because his vision flies in 
the face of all known science, and to me at least is actually 
inconceivable.

JD