[CAUT] Wire Stretch

[RicB]

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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