Helmholtz and Steinway

[John Delacour]

At 9:51 PM +0100 11/18/01, Richard Brekne wrote:

>Taken from the Conklin article you refer to below is the following 
>quote, which he basically says two or three times over in the case 
>on non wound strings. It seems to me that Conklins statement is in 
>conflict with your own about the termination points having no effect 
>on the horizontal mode JD. Otherwise how can Conklins statement that 
>it is the length of the speaking length that determines the 
>frequency of the longitudinals ?

Well I'm as keen to get at the facts as you and others are, Richard. 
It is not going to be easy without some experimentation and it will 
take a while to set that up.  If anyone else, such as Stephen, has 
more experimental data on this topic, I'd lovree to know about it.


>I also seem to remember that Rons reading of the other Conklin 
>article is also correct, having read that myself a couple times a 
>year ago. I have it at the University and will check this again. But 
>I dont think I remember it ever being stated that Longitudinal modes 
>are uneffected by the terminations. But we will see.

Well Stephen has suggested a simple way of showing this and it seems 
to me pretty obvious that compression waves travelling the length of 
the wire will not be stopped by impediments to transverse movement. 
Imagine a thick steel rod six feet long passing through a one foot 
cube of concrete in the middle of its length which prevents any 
sideways movement.  You put your ear to one end and I'll tap the 
other with a small hammer.  You are suggesting that you will hear 
nothing that is due to waves travelling along the rod.  I think that 
unlikely.

I feel that more experimental data is needed.  Conklin is concerned 
primarily with the audible longitudinal waves in covered strings and 
his demonstrations are borne out to a degree by my own experience as 
a bass string maker.  To that extent I find his thesis interesting, 
particularly in view of the actual proofs he uses.  On the other hand 
he fails to mention other aspects of string design which, in my 
experience, have a greater effect on tonal quality in covered 
strings.  All Conklin's demonstrations are done with low bass notes.

We then make the jump to Theodore Steinway's longitudinal waves, 
which are right at the other end of the scale, from A4 (440c/s) 
upwards and not dealt with at all by Conklin.  According to Conklin 
the frequency of these waves would be roughly 7000 c/s rising to over 
60,000 at C (4186 c/s).

You wrote, quoting from Conklin:

>  "The longitudinal frequency of a plain steel string in a piano can 
>be changed only by altering its speaking length..."

Since he produces no demonstrations relating to plain wire strings, 
it is quite possible that he would need to prove that this would make 
a difference if it did not alter the TOTAL length of the wire.  Nor 
are we told how these longitudinal waves are initiated, how they are 
affected by the relative tension of the wire etc.  He leaves more 
questions unanswered than he solves, though what he does show is 
interesting.

JD