[CAUT] Wire Stretch

[John Delacour]

At 12:50 am +0100 2/5/07, RicB wrote:

>Hi JD
>
>Since you havent responded to this...for the simple case of the 
>deflection alone... the change in tension (with a starting tension 
>of  157 lbs and frequency of 2105 hz, lengths as per yours below) 
>for a 0.5 mm drop in deflection is about 19 hz. The strings length 
>will shorten by about 0,018752 mm which immediatly lowers tension by 
>roughly 2,8283 lbs.  Using the formula =SQRT((T*398*10^6)/(length in 
>mm *string diameter in mm )^2) for frequency then... you get about 
>19 hz change.  Works out the same using your formula for F and a 
>value of 18036 for K.
>
>Quite a big difference from your 0.026 hz I'd say.

Yes,  I'm afraid since then I have been occupied full time with 
developments at my new workshop on the farm -- a converted silo -- 
and have had little time to devote to the matter.  You are, of 
course, right about the drop in tension needing to be considered. 
The actual quantities, of course, will depend on the original and 
changed configuration in a particular case

>   You can actually measure this on a monochord if you like... very 
>easy to construct something to do this I would think.

Yes indeed.  When I move into the silo, I hope at the end of this 
month, there are many experimental set-ups I hope to make room for -- 
things I have been meaning to do for ages like a wire breaking-strain 
machine.  Space is such a problem for us piano people and I'm hoping 
that if I'm careful with my 140 square metres I'll me able to move 
about for a change and do some long-delayed tests.

>If anyone wants a copy of the basic spreadsheet worked out to 
>calculate this stuff using the formulas supplied by Galembo I'd be 
>glad to share it with you and welcome comments.

Send it along.

All that said, I am not convinced this particular measurement is of 
the greatest significance, since it is only one part, and a very 
small part, of a combination of things -- unequal tension on the two 
sides of the bridge, down-bearing equilibrium, bridge admittance, 
termination quality etc.  The question of wire strength, elasticity 
and stretching with time and differential elasticity according to 
varying stress is another matter, and one which can be considered in 
isolation.  A long series of tests for this would be very 
informative.  May great minds from Galileo to Timoshenko have 
revealed most of the secrets we would like to know, and I have no 
doubt that if Timoshenko were alive and on this list we would very 
quickly get most of the answers we needed, not only about wire but 
also about soundboards, but the intuitive wisdom of the craftsman 
often covers ground that is not covered in the most learned of 
scientific treatises.  It is when the scientist and the craftsman 
both apply themselves to a particular phenomenon that advances really 
can be made.

JD