[CAUT] Wire Stretch

[RicB]

No John

He does not just use Pythagoras' theorem just as you did.  And if you 
stop up and look closely I am sure you will understand this.  When you 
change the deflection you change three things... its length, tension, 
and frequency. The new length you can calculate just as you did.  But 
that leaves you with two unknowns... the new tension and the new 
frequency. None of your formulas can calculate one without the other.

Galembos formula does something entirely different.  It finds the change 
in the amount of tension in the wire cause by the change in string 
length. Once you have this figure... then you can calculate for 
frequency using your formula. 

But you cant just change the length of the string and without further 
ado use the formulas you give... they dont deal with two unknowns.  I'll 
let you work it out... and find the error in the documents last line I 
pointed out to Alex when I first got it.... just a typo... but important 
to get right.

Cheers
RicB

        At 5:51 pm +0100 29/4/07, RicB wrote:

         >Unfortunatly, you can not calculate the change in frequency for
         >change in string deflection this way. Or so I am told by a few of
         >the worlds physisists.  Please see the following for what
        according
         >to these is a more correct way of doing this.


    <http://www.pianostemmer.no/files/String%20deflection_files/brekne.doc>

    Your "world's physicist", in the file above, uses Pythagoras' theorem
    and no other principle, just as I did, to calculate the changes in
    length.  The only difference in his equations is that he takes into
    account a change in length behind the bridge, considered as a violin
    bridge and not a piano bridge.  Clearly some slight difference in the
    results will arise if that is added in, with corrections for the
    actual disposition of the string on a real bridge, just as the
    re-angling of the dogleg 1/2mm lower round the slanting front pin on
    a real piano bridge will make a difference, but I'm at a loss to
    understand why you consider your famous person's Pythagorean theorem
    so superior to mine and intrigued to see your worked example and
    results based on this document.

    If, for instance, you take C76 with a speaking length of 100mm, as I
    proposed, and take into account a back-length of 50mm, with an
    initial deflection of +1.5mm (i.e the soundboard bridge is 1.5mm
    above the straight line from hitch-plate bearing to top bridge), what
    exact results do you get, using your valued equations, when you force
    the string down 1/2mm into the wood of the bridge at the front pin?

    JD


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