Derive wave velocity equation from wavelength, surface tension and density

[ahmedb]

The velocity of waves in a liquid depends on the wavelength λ, surface tension γ, and density ρ, of the liquid, Derive an equation to relate v, with wavelength, surface tension and density, (note: surface tension, has a formula of force per unlit length and SI unit of Nm^-1)

 

[PeterO]

The velocity of waves in a liquid depends on the wavelength λ, surface tension γ, and density ρ, of the liquid, Derive an equation to relate v, with wavelength, surface tension and density, (note: surface tension, has a formula of force per unlit length and SI unit of Nm^-1)

reducing to fundamental units

λ - m
γ - N.m^-1 = kg.m.s^-2.m^-1 = kg.s^-2
ρ - kg.m^-3

The final answer is velocity, so m.s^-1

If you multiply all three together [ie λ x γ x ρ] we have m x kg.s^-2 x kg.m^-3 = kg².s^-2.m^-2

Not quite what we wanted. We needed the kg to cancel out, so one of γ or ρ needed to be in the denominator.

The fact that all units were squared doesn't matter - we can throw in a √ at the end to fix that.

have a play round and see how you get on.