# Dimensional analysis and buckingham pi theorem

I'm trying to find a function in the following way:

$$F = f(I, f, m, V, A, L)$$

Where $$I$$ is sound intensity, $$f$$ frequency $$m$$ mass, $$V$$ volume, $$A$$ area, $$L$$ length.

So I wrote down:

$$M^1 L^1 T^{-2} = [T^{-1}]^a [M T^-3]^b [M]^c [L^3]^d [L^2]^e [L]^f$$

Then I get the equations:

$$M: 1 = b+c$$

$$L: 1 = d+e+f$$

$$T: -2 = a -3b$$

There are too many unkowns to solve this and get the formula. Can someone help me please? Thanks in advance

• The Pi theorem states that since you have 3 dimensions $(M, L, T)$ and 6 parameters, you can form $6-3=3$ dimensionless groups. Not all the parameters may be used in a group. From there it's a game of intuition and guessing until you get something that works. And even then, the group formed may or may not have physical relevance. This process is typically guided by empirical data and theory, not just ex nihlio. Jan 4, 2022 at 22:47
• @RC_23 … looks to me like an excellent answer… Jan 4, 2022 at 22:53
• THanks for the answer. How do you exactly proceed then? I'm looking at this example. How do you form the pi groups exactly? Jan 5, 2022 at 9:15
• I responded as an answer Jan 7, 2022 at 2:07

In your case, what is $$F$$ physically? What that is will help guide you in the relationships to expect. Based on your parameters, you can make a geometric parameter $$V/(AL)$$ that is dimensionless for example. $$I$$ is already dimensionless I believe.