[CAUT] String scaling help svp?

[Ric Brekne]

Hi Stephen

Thanks for the first direct reply to this point. Tho there a couple of 
points I am unclear on and I wonder if you could clarify. It almost 
seems like you are saying that Youngs Modulus for pianostrings is 
essentially indeterminable (for all practical matters) and that Youngs 
Inharmonicity coefficient is in error to begin with.

To the later,  If you look at the paragraphs surrounding equations 8 and 
9, Young clearly states that there is a direct relationship between Q 
and D.  And in your example of Brass, Q (Youngs Modulus) should indeed 
be lower (then steel) as a result of its higher density.

Young goes on in the later part of the paper to take an example from one 
manufacturer who gives a spec for Youngs modulus that fits nicely that 
same manufacturers spec for density if one employs the relationship 
Young describes in/around equation 9 in his paper.

So... what is wrong with Youngs paper then...?  Why is the relationship 
Q/p = 25..5*10^10th that he gives not valid ?

Thank you kindly

RicB

     >According  to Youngs paper of 1952 the Modulus divided by the
     >density of the string results in a consant (25.5*10^10th). It
     >appears to me that this constant is supposed to be the same
     >regardless of material, which would mean that E is the product of D
     >* this constant.

    Ric,

    Young's modulus is not an easy parameter to determine experimentally.
    Using bulk tensile testing, even with fancy equipment, you can't get
    a very accurate value, partly because real materials never behave
    completely linearly (even steel wire). There are additional
    complications that make tensile testing of wire a very difficult
    experimental procedure, adding to the inaccuracies in determining the
    modulus for a wire specimen.

    It is primarily a material dependent property, but can be affected to
    some extent by mechanical working (and heat treatments).
    Consequently, a small range of moduli will be relevant for a given
    material according to how it has been physcially processed. Accurate
    measurement of Young's modulus can be done by sonic and similar
    techniques which measure the vibrations of the metallurgical
    structure at the atomic level. All are involved and generally
    expensive. There is no general correlation between density and
    modulus. Compare brass, denser but the modulus is considerably lower
    than that of steel.

     >In any case it seems to me that there is some significant  amount
     >of confusion surrounding Young Modulus and it perhaps is more
     >important in a practical  scaleing sense then we assume.

    It has little practical use for scaling since it is not a
    controllable factor in wire manufacture. It is essentially determined
    by the choice of material.

     >This fits well with your call to empirical testing for breaking
    strength / %'s

    The only way to determine the capabilities of your wire is with
    tensile testing.

    Stephen
    -- 
    Stephen Birkett
    http://real.uwaterloo.ca/~sbirkett