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The formula is:

$$ f = \frac{3.5161}{2\pi L^2}\sqrt{\frac{EI}{\rho A}} $$

$A$ = area, $\rho$ = density, $I$ = second moment of area cross section, $E$ = Young's modulus, and $L$ = length. Can anyone help transpose this equation so that A is the unknown subject?

I can't find my way around it, and the people I've asked are stumped?

So i have some sprung steel, I'm calculating the frequency to make a SPECIFIC note.... but i want to know what size I need my steel (rectangular rod) to be to create the desired note/frequency.

Am I looking at it all wrong?

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closed as off-topic by tpg2114, Kyle Kanos, Yashas, David Hammen, sammy gerbil Mar 10 '17 at 1:52

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  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – tpg2114, Kyle Kanos, Yashas, David Hammen, sammy gerbil
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Please check that the edited formula is still correct. $\endgroup$ – Mark H Mar 9 '17 at 15:29
  • $\begingroup$ Perfect, thank you Mark. Sorry I'm new to this, and very rusty with the old engineering maths. $\endgroup$ – Dale Mass Mar 9 '17 at 15:32
  • $\begingroup$ Out of curiosity, what instrument is this for? Xylophone? $\endgroup$ – Mark H Mar 9 '17 at 15:40
  • $\begingroup$ I'm a craftsman, it's a mixture between a Kalimba (Mbira) and a Cajon drum. I want to be as accurate as possible making the Steel "keys". Unsure about the Length. I've been working on various tests all week. $\endgroup$ – Dale Mass Mar 9 '17 at 15:48
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$$ f = \frac{3.5161}{2\pi L^2}\sqrt{\frac{EI}{\rho A}} $$ $$ f^2 = \left(\frac{3.5161}{2\pi L^2}\right)^2\frac{EI}{\rho A} $$ $$ Af^2 = \left(\frac{3.5161}{2\pi L^2}\right)^2\frac{EI}{\rho} $$ $$ A = \left(\frac{3.5161}{2\pi L^2}\right)^2\frac{EI}{\rho f^2} $$ or $$ A = \left(\frac{3.5161}{2\pi L^2f}\right)^2\frac{EI}{\rho} $$

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  • $\begingroup$ Mark H, extremely helpful, the workings out makes it perfect to revise. You've really helped me out, thank you. $\endgroup$ – Dale Mass Mar 9 '17 at 15:40

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