Where: f is the frequency the fork vibrates at in Hertz. (close to the name of the inventor: Max Hetzel:D)
A is the crosssectional area of the prongs (tines) in square metres.
l is the length of the prongs in metres.
E is the Young's modulus of the material the fork is made from in pascals (stiffness).
ρ is the density of the material the fork is made from in kilogrammes per cubic metre.
Read Alpha symbol as = sign
So what does this mean for the accuracy of these factors in practice and values plus tolerances?
Since L is powered by 2, it seems to be the most influential.
We already know that the frequency may not deviate more then 1/1e5 Hz to have an Accutron running as accurate as better then 60 seconds a month.
So let's do some calc on the length tolerance, assuming that all other factors are constant (which in practice ofcourse they are not)
Constant factor values:
A : 1E6 m
E : 2E11 Pa
ρ : 3,95E+06 Kg/m3
Variable factor
L : 25 mm. = 2,5E2 m
If we use these values in the formula we get: F= 360 Hz
(i had to adjust density to get to a frequency of 360 Hz, since an Accutron tuningfork is not a standard tuningfork, because of the magnets at the end of the tines/prongs)
Now lets see what happens to the frequency when we adjust the length of the tines/prongs with as little as 0,01 of a millimeter:
According to my Excelsheet the frequency will drop to 359,71 Hz. Assuming my calculations are correct, you get and idea of how (in every factor that influences the frequency) extremely accurate an Accutron tuningfork must have been manufactured.
I think that the more you know and understand about Accutrons, the more unbelievable it is that it has ever worked, let a lone in mass production.
