v, T, ρ and λ denote speed, surface tension, mass density and wavelength, respectively. In an experiment v depends on T, ρ and λ, respectively. The value of v is proportional to

v = KTaρbλcLHS = [M0LT-1]RHS = [MT-2]a[ML-3]b[L]c         = [Ma+bL-3b+cT-2a]According to homogeneity principle,LHS = RHS∴   [M0LT-1] = [Ma+bL-3b+cT-2a]∴ a+b = 0∴ a = -b    ------(i) -3b+c = 1  ------(ii)-2a = -1  ---------(iii)∴ a = 12∴  b = -a = -12       -3b+c = 1∴  c =- 12∴  v = KTaρbλc   = KT12ρ-12λ-12   = KTρλ