[CAUT] Young Modulus / Density in piano wire

[RicB]

Hi Folks

Attached is the easily read article by Young from 1952.  In particular I 
wish to draw your attention to the paragraphs which are attached to 
equations 8 and 9 where these two yield the following interesting 
relationship.

Q/p = 25.5 *10^10
(relationship 1)

Q being the Young Modulus and p being the string density.  I use dynes 
/cm^2 for Q and  gm per cm^3 for p as in Youngs paper.

This relationship implies directly that if one has the value for either 
Q or p one can calculate the other. And indeed later on in his paper in 
the 7th paragraph of the section entitled Three Steinway Pianos he does 
just that citing a Q value of 20.0 * ^11 dynes per cm^2 and a density of 
7.83 g/cm^3.

If one on the other hand one uses the values for the Youngs Modulus and 
densities found in McFerrin one comes up with a very significant error 
in regards to  relationship 1.  The same kind of error occurs if one 
uses the published wire data on Pure Sounds site for all types of wire 
he gives data for, and just about everywhere you look outside of Youngs 
own paper.

The point is that Youngs equations in the paper from 1952 in particular 
his equations relating to B (the coefficient of inharmonicity) yield the 
relationship above (relationship 1).  If there is more then slight 
divergence in the relationships between the real (measured) for Q and p 
compared to Youngs formula for B... then something must be wrong with 
the formula itself..... OR... the measured values are in error.

I would think the later is more likely when it comes down to it ....  so 
the question is which of the measured values (Q or p) we see out there 
in the world is more likely to be the most dependable ?  I would guess 
at density (shot in the dark really)... in which case if one knows 
(accurately)  the density of the material then its Youngs modulus is a 
GIVEN....a direct result of the relationship above (1).   It HAS to 
be... or Young was wrong.

Comments are very welcome.

Thanks
RicB


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