Rocking bridges

[John Delacour]

At 9:49 PM -0600 12/23/01, Ron Nossaman wrote:

>Fully strung piano, up to pitch. A beam spanning the rim, with a 
>laser pointer mounted to it instead of a dial indicator. ...It's not 
>much, but the bridge rocks forward each time. The higher the 
>ceiling, the greater the movement and the easier to see.

For some reason, a message I posted yesterday to the list did not 
return to my mailbox, so I've sent it again.

This message shows a model that demonstrates very simply, without 
lasers or pianos, exactly the phenomenon you are talking about, about 
which there is no argument. Any continuous force, however slight, 
acting on a system in equilibrium will, by well-known physical laws, 
cause that system to change position until an equal and opposite 
force is encountered.

I have said from the outset and have been forced to repeat numerous 
times, in response to suggestions that I have denied it, that the 
movement of the bridge occurs.  By the same token the bridge in 
rocking will obey the same physical laws.  How can you still pretend 
that there is any argument about this.

My model was designed so that those unfortunate people without lasers 
and mirrors could see for themselves what it is not possible to see 
with the naked eye and furthermore carry out tests that would be 
impossible on a strung grand without highly sophisticated measuring 
equipment:

At 10:51 PM +0000 12/23/01, John Delacour wrote:
>To simplify things I thought it would be a good idea to eliminate as 
>far as possible any impediment to the bridge's rocking, such as the 
>tension of the other strings and the fixing to the soundboard, so 
>the drawing above shows a string (s) of some material stretched 
>between two pins (p) and passing over a bridge (b) that is curved at 
>the bottom to allow it to rock and roll. The string (s) cannot slide 
>over the bridge top.  Out of the top of the bridge comes a needle 
>(n) that ends in a pointer (a) running round a scale (d).  Clearly 
>if pressure is applied to the string at s or anywhere, the pointer 
>(a) will move clockwise as the bridge (b) rocks and will return to 
>zero when the pressure is released.  The base can be considered 
>anything fairly rigid and is not pertinent to the design; it is in 
>no way to be considered a representation of a soundboard.

This description is precisely what you are describing.

My model does not involve the soundboard; in fact up to now I have 
not been concerned with the soundboard, as I have also repeated.

At 8:01 PM +0000 12/16/01, John Delacour wrote:
>In my most recent message, I have not involved the soundboard.  In 
>the picture I have painted so far, I have made no mention of the 
>soundboard except in my last paragraph as a trailer to the next 
>episode ...
>
>...And there is the profound difference between us.  I do NOT see a 
>string physically moving and rocking a bridge and driving the board 
>as a solenoid [read 'voice coil' ] drives a cardboard cone.  I 
>contested the analogy from the very beginning and do so now.


At 11:37 AM -0600 12/16/01, Ron Nossaman wrote:
>In making a bridge super stiff, it can be made too massive, which
>can negatively affect the system. ... The diaphragm action is 
>primarily cross grain to the panel ...
>... I see a string with an (initially) vertically oriented transverse wave
>... physically moving the bridge, which physically moves the 
>soundboard, which physically moves the bridge, which physically 
>moves all of the strings in the system.

No experienced piano technician can be unaware of the fact that the 
degree of rigidity of the system is crucial, as we know from numerous 
practical proofs.  If the bridge(/soundboard) were totally rigid, all 
the sound of the string would be reflected at the bridge and we would 
hear nothing but the 'unamplified' sound produced by the air the wire 
compresses.

But you claim and have claimed all along that the transfer of the 
sound from string termination to soundboard is achieved by "physical 
movement" of the components, that the movement initiated by the 
string sets up a correlate movement of the bridge and hence of the 
soundboard.

I have had to say again and again that the movability, flexibility, 
non-rigidity, call it what you will, of the bridges and the 
soundboard has never been at issue.  Bring in the bridge-pins too if 
you like; there will be no argument.


Since there seems to be a problem getting the message containing the 
gif to the list, here are URIs for the images:

First picture: <http://www.pianomaker.co.uk/images/rocbrig1.gif>
Second picture: <http://www.pianomaker.co.uk/images/rocbrig2.gif>

A length of rubber band or elastic can be stretched over the bridge 
as the string and this can be weighted with a bit of metal or split 
shot to allow a lower vibration frequency to be produced.  When the 
'string' is excited, it will vibrate transversally, whether 
vertically or horizontally or both is immaterial.  At the same time 
the bridge will rock as its equilibrium is disturbed by the strings 
movements, tension changes etc.  The pointer will describe an arc on 
the dial as this happens.

It will become immediately clear that the frequency at which the 
bridge rocks bears no relation at all to the frequency at which the 
string is vibrating or to any of its partials.  In the second picture 
you will see that I have fixed a weight to the needle, and it is 
hardly necessary to say that this will alter the frequency of the 
bridge's rocking, just as the weight of a metronome.  Any number of 
different devices could be used to lower or raise the period of the 
bridge's motion, but the frequency of the vibrating string will 
remain within a constant range, experiencing unpredictable 
fluctuations, of course, as a result of the bridge's moving.

Now I ask you or Del or Ron O. or anyone to explain to me how this 
movement (in this case rocking movement) can be in any way 
instrumental in the production of sound waves at the frequency of the 
vibrating string.

JD