Posted by not done it yet on 25/09/2022 11:03:18:
One has to remember that the note will not only depend on the tension, so different notes will emanate from different lengths of free band. Certainly once you know the note for your particular band, it should be straight forward – unless you change its width or thickness, I suppose.🙂
Yes, the frequency is inversely proportional to the free length, but it turns out (if – and it's getting to be a bigger and bigger if as I get older!) my calculation is right the the stress/fundamental frequency relationship is independent of the width and thickness of the blade. I get:
sigma = 4 x L^2 x f^2 x rho
where sigma is the stress, L the free length, f the frequency and rho the density of the blade material.
Posted by duncan webster on 26/09/2022 00:22:46:
Google Mersenne's law, it tells you the relationship twixt frequency, mass per unit length and tension. I suspect it will be a bit off as a saw blade has inherent stiffness unlike a string. Some bright person might work it out if having trouble sleeping.
Good point – the result above was based on the Mersenne's law, though I didn't know the name for it. My gut feeling is that the zero tension beam strength of a bandsaw blade is negligible compared to the tensioned strength, but I shall investigate that when next I have a sleepless night and a coincident fit of brightness. Don't hold your breath! I shan't.
After starting this thread I remembered that I had splashed out a fiver or so on something called a Lindley extensometer at a junk shop some years ago. It looked interesting, but has since been gathering dust:

I think that this is functionally equivalent to the device in Gary's article, so I should be able to make measurements myself. However, having a look around I see that the Science Museum has something similar but with an extra part:

Can anyone suggest what that part does? There is no indication of anything missing (eg redundant threaded hole in the casting) in my example.
Robin
PS the second image was downloaded from the Science Museum and has been altered to the extent of adding a red arrow to indicate a particular part.
R.
Edited By Robin Graham on 27/09/2022 02:26:35