The dependency of speed of water surface waves (capillary waves) on...

Velocity of surface waves depends on density of water, its own wavelength of surface tension.

$v ∝ {ρ}^{a}{\lambda}^{b}{\gamma}^{c}$

\left[LT^{- 1}\right] ∝ {\left[ML^{- 3}\right]}^{a}{\left[L\right]}^{b}{\left[\dfrac{MLT^{- 2}}{L}\right]}^{c}$<br /><br />\left[LT^{- 1}\right] ∝ M^{a + c}L^{- 3a + b}T^{- 2c}$

$a + c = 0 ..........(i)$

$- 3a + b = 1 .............(ii)$

$- 2c = - 1 .............(iii)$

Solving
$a = - \dfrac{1}{2}, b = - \dfrac{1}{2}, c = \dfrac{1}{2 ,}$

$v ∝ {ρ}^{- \dfrac{1}{2}}{\lambda}^{- \dfrac{1}{2}}{\gamma}^{\dfrac{1}{2}}$

$v ∝ \sqrt{\dfrac{\gamma}{ρ\lambda}}$