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
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