[CAUT] Wire Stretch

[Leslie Bartlett]

Mail me privately, off list, would you. It's a waste of list time for my
silly question. Thanks
les

  _____  

From: caut-bounces at ptg.org [mailto:caut-bounces at ptg.org] On Behalf Of RicB
Sent: Sunday, April 29, 2007 6:21 PM
To: caut at ptg.org
Subject: [CAUT] Wire Stretch


Hi Les...

First let me say I understand your feelings here... but if you get hooked on
figuring out this stuff you probably will find you are far brighter at math
then you may think now. Secondly let me say that after re-reading your
post... this bit of math doesnt quite address what you were asking for. This
is about finding the change in string tension that occurs when one deflects
or changes the deflection of a string and doing nothing else.

Delta is a greek word used in math for <<change in>>  Usually denoted by a
triangle.  Not a big thing really. So the first bit below is simply 

<<the change in Tension>> = Youngs Modulus * Cross Section of the string *
<< the change in the string length because of the deflection >> divided by
the origional length of the string.

Not so tough really.. just some multiplication and division.

The second bit is much of the same thing 

Frequency = the square root of (Tension divided by (the length of the string
squared times the diameter of the string squared times the strings density
constant)

You can use McFerrins book to find out a good deal about some important
formulas we use.  A bit of head scratching and insistance on digging out
your high school pre-calc and algebra books will take you a long ways. 

I can send you a spread sheet that does all this if you like...

Cheers
RicB



Uh, there's a reason I did poorly in math...........  But I know some folks
who can tear this apart step by step.... thanks
lse 





I just posted a link to a such an approach.  In the end its quite easy.  
You first find the change in tension a give change in deflection yields, and
then you have all you need to use standard frequency formulas.

 Delta T = ES (Delta L / L). 

Then calculate for the new frequency with your known wire diameter, speaking
length and tension and the so called K constant... which in this case is

    (Pi * string density / 981)

f = Sqrt(T/(L^2*d^2 *K)

Ok ?

Cheers
RicB

Is there some source or "relatively easy" formula for calculating how much a
string must move through a termination point to produce pitch change?    I'd
like to have some tiny bit of basic information so that in describing pitch
corrections of significant distance I can use the information to explain the
likelihood that the piano will need a retuning in the near future.
thanks
les bartlett



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