Wavelength of surface waves in terms of surface tension, density and frequency

[pisiks]

Homework Statement

The wavelength of $$\lambda$$ of waves on the surface of a water on a cup has three variables:
surface tension of the water $$\sigma$$, water density $$\rho$$, and frequency of vibration f. Deduce the relationship of these three variable to the wavelength.

Would the same relationship hold if you were on the moon?

Homework Equations

$$\lambda$$ = $$\lambda$$($$\sigma$$, $$\rho$$, f)

The Attempt at a Solution

 

[rock.freak667]

I think you can use the Buckingham-pi theorem here but I don't quite know how it works

But normally I'd do this

$$\lambda = k \sigma^a \rho^b f^c$$

then write everything in tersm of the fundamental units and equate the units on the LHS and RHS