[CAUT] Wire Stretch

[John Delacour]

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