[CAUT] Scientific study - Stainless wire (Help!)

[Richard Brekne]

Hi Jurgen.

Breaking strength is also dependent on some other bits and pieces of 
wire physics, in particular the Youngs modulus. I spent a couple months 
trying to figure out with my own limited math and physics how both the 
Youngs modulus and the string density figures could be so different 
depending on where you looked.... and how they actually worked out in 
some of these formulas.

Again, using McFerrin... this time the inharmonicity for plain wire 
given there.  It became apparent to me that looking at equation 4-2 on 
page 43 that one could calculated Youngs modulus directly from String 
density... or the other way around depending on what was <<known>> ahead 
of time.  I posted quite a few querries on the matter a year or so back 
because doing so seemed to be exactly what Robert Young himself did in 
his own paper on the modulus and yet in real life you not only run into 
wildly variant values for Youngs modulus and  average density for piano 
wire is, but if you plug in the values for other potentential string 
material the Inharmonicity given by McFerrin no longer seemed to work. I 
talked a bit with the author of Bonemens about this and he citied this 
as one of his main reasons for not even bothering including bass strings 
in his scaling program. Inharmonicity was dodgey enough for plain wire 
but for bass strings just useless was his reasoning.... struck me as 
going a bit too far but just so.

In anycase,  as to your specific question.  The apparent difference in 
string density given the figures I cited does seem quite low yes, and 
would as such tend to lead one to think that difference boarders on 
being less then significant. It is ususal to simply combine the values 
for PI, String density and acceleration into a constant. That is 
(PI*String Density / 981))  when Length and diameter is in cm ^2.   For 
regular wire this works out to 0.02513.  Pure sound ends up at 0.02530.  
The tension formula then becomes T = f^2 * L^2 * d^2 * K, where K is the 
constant just mentioned, and L and D are in cm^2, and T is given in 
grams of force.  I'll leave it to you to see if your 0.64% idea works 
out in the resultant tension. :)

Jauns version of this utilizes tension in Kilograms (a bit more 
practical as an end result) But then his measurements for L and d are in 
meters ! and the gravity acceleration is  9.81 instead of 981.  I 
suppose that last bit can get a bit confusing when trying to sort all 
this out by oneself, as the 981 figure is a specific physics quantity.  
981 centimeters per second per second.  Also, one gram of force 
corresponds to 981 dynes of force.  Dynes is a physics quantity usually 
used to express tension... its just folks like piano scalers who find 
that quantity awkward and insist in using kilograms or pounds instead.

Actually guys,  Jim you mentioned this about understanding math.  I 
flunked high school maths hated classes.  In first years of college I 
found that I actually did like algebra and took a couple classes and did 
quite well.  But I never really followed up.  In my later years I have 
thrice tried to find time to get back into it because its really just an 
enormous and fantastic puzzle game... but one has to make a living as 
well.... so I have managed to get into that pre-calculus stage that all 
of us are supposed to learn by our senior year of high school.  None of 
the maths or physics I've seen discussed over the years here really even 
get close to that (with very few exceptions).  I would suggest we 
underestimate our abilities to digest these maths and physics concepts 
and skills.  Setting off a bit of time here and there and digging 
through ones high school levels books to figure out a problem puts you 
on the road.  Go for it.

Cheers
RicB


    My math is probably wrong on this and I'm sure I will be corrected if 
    that is the case.  But as I see it, the difference in string density 
    between Pure Sound and standard wire is less than 0.64%

    Wouldn't that, according to the McFerrin formula, result in tension 
    that is 0.64% higher?  And is less than one percent really enough to 
    make a noticeable jump that much closer to the breaking strength?
    Help me out on this one...

    Jurgen Goering
    Piano Forte Supply
    (250) 754-2440
    info at pianofortesupply.com <https://www.moypiano.com/resources/#archives>
    http://www.pianofortesupply.com