[CAUT] Wire Stretch

[RicB]

Hi JD

Since you havent responded to this I thought I would supply the answer 
you querried. This answer takes into consideration only the tension and 
frequency change brought about by the deflection change you sketch out 
below.  It doesnt take into consideration that the strings offset angle 
through the bridge pins will also change by such a 0.5 mm sink into the 
bridge... and hence its length for this segement changes significantly 
altering the pitch and tension further and in the same direction. 
But...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.  You can actually 
measure this on a monochord if you like... very easy to construct 
something to do this I would think.

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. 

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.Ê
     >
     ><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


-------------- next part --------------
An HTML attachment was scrubbed...
URL: https://www.moypiano.com/ptg/caut.php/attachments/20070502/6cf7fa8e/attachment.html