The speed (v) of ripples on the surface of water depends on surface tension$\left(\sigma \right)$, density $\left(\rho \right)$

            and wavelength$\left(\lambda \right)$. The square of speed (v) is proportional to        

$$\begin{gathered} Let v\propto {\sigma }^a{\rho }^b{\lambda }^c \\ Equating dimensions on both sides, \\ \left[M^0{L}^1{T}^{-1}\right]\propto {\left[M{T}^{-2}\right]}^a{\left[M{L}^{-3}\right]}^b{\left[L\right]}^c \\ \propto {\left[M\right]}^{a+b}{\left[L\right]}^{-3b+c}{\left[T\right]}^{-2a} \\ Equating the powers of M, L, T on both sides, we get \\ a+b=0 \\ -3b+c=1 \\ -2a=-1 \\ Solving, we get \\ a=\frac{1}{2},b=-\frac{1}{2},c=-\frac{1}{2} \\ \therefore v\propto {\sigma }^{1/2}{\rho }^{-1/2}{\lambda }^{-1/2} \\ \therefore v^2\propto \frac{\sigma }{\rho \lambda } \end{gathered}$$