The dependency of speed of water surface waves (capillary waves) on the density of water ( ρ ) their wavelength ( λ ) and surface tension ( γ ) is -

Step-by-step solution

Velocity of surface waves depends on density of water, its own wavelength of surface tension. v ∝ ρ a λ b γ c L T - 1 ∝ M L - 3 a L b M L T - 2 L c L T - 1 ∝ M a + c L - 3 a + b T - 2 c a + c = 0 ..........(i) - 3 a + b = 1 .............(ii) - 2 c = - 1 .............(iii) Solving a = - 1 2 , b = - 1 2 , c = 1 2 , v ∝ ρ - 1 2 λ - 1 2 γ 1 2 v ∝ γ ρ λ