The speed (v) of ripples on the surface of water depends on surface tension $\left(\mathrm{\sigma }\right)$   density ($\mathrm{\rho }$)  and wavelength ($\mathrm{\lambda }$) . The square of speed (v) is proportional to 

Let  $\mathrm{v}={\mathrm{\sigma }}^{\mathrm{a}}{\mathrm{\rho }}^{\mathrm{b}}{\mathrm{\lambda }}^{\mathrm{c}}$

Equating dimensions on both sides

$\left[{\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^{-1}\right]={\left[{\mathrm{MT}}^{-2}\right]}^{\mathrm{a}}{\left[{\mathrm{ML}}^{-3}\right]}^{\mathrm{b}}{\left[\mathrm{L}\right]}^{\mathrm{c}}$

$\propto {\left[\mathrm{M}\right]}^{\mathrm{a}+\mathrm{b}}{\left[\mathrm{L}\right]}^{-3\mathrm{b}+\mathrm{c}}{\left[\mathrm{T}\right]}^{-2\mathrm{a}}$

Equating the power of M,L, T on both sides, we get

a+b = 0

-3b+c = 1

2a = -1

Solving, we get

$\mathrm{a}=\frac{1}{2},\mathrm{b}=-\frac{1}{2},\mathrm{c}=-\frac{1}{2}$

$\therefore \mathrm{v}={\mathrm{\sigma }}^{\frac{1}{2}}{\mathrm{\rho }}^{\frac{-1}{2}}{\mathrm{\lambda }}^{\frac{-1}{2}}$

$\therefore {\mathrm{v}}^2=\frac{\mathrm{\sigma }}{\mathrm{\rho \lambda }}$