[CAUT] Wire Stretch

[RicB]

Okay guys... sorry bout the first post... hit the send button by mistake..

Heres what I come up with.  I'm going to assume a Youngs modulus for
piano wire in accordance with McFerrin, which is the lowest I've run
into so far out there.

For a 0.8 mm Ø string of 150 mm long speaking length, 50 mm back
length... and tension at 150 with zero deflection, a 5 mm deflection
will increase tension to 189 lbs, cause a frequency change of 248 hz
(from 2057 to 2305) and impose a 28 lb bearing force on the point of
deflection.

For a string 0.9 mm Ø 500 mm long speaking length and 100 mm back length 
  the same scenario causes an increase in tension of 5 lbs, frequency 
increase of 6 hz and a bearing on the deflection of 9.3 pounds

For a string 1.2 mm Ø 1000 mm long speaking length, and 100 mm back 
length the same scenario causes an increase in tension of 4,3 lbs, 
frequency change of 2 hrz and 8.5 lbs  of bearing on the deflection.

Interesting to note... for this last example if the back length is 50 mm 
and all else is the same.. then the change in tension is 8.75 lbs, 
frequency change is 4 hrz and bearing at the deflection point 16.6 lbs


Clearly a short back length inhibits the soundboards ability to deflect 
the string more then a longer backlength does.. by quite a bit.

Another point is that 150 lbs tension is pretty low.. and in the range 
the lower tenor strings have. These low tenor plain strings experience 
very large frequency changes that simply can not be accounted for by 
even a 5 mm deflection change. The high strings have a much higher 
starting tension... if for example I use a real life tension on the 
first example... about 165 lbs.. we get a tension increase of 39 lbs, 
frequency rise of 237 hz and bearing of 30 lbs. The change in % breaking 
tension is about 10 %... and the difference between this and the first 
example are not all that large... at first glance something about the 
assumed significance of % breaking tension on pitch change doesnt quite 
add up.

More food for thought

Cheers
RicB