Clean pond water has surface tension N m

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Waves, acoustics and compressible flow · Waves, acoustics and compressible flow

Fluids and Continuum Physics, Ch Surface gravity and capillary waves

Problem

Clean pond water has surface tension γ=0.073\gamma = 0.073 N m−1^{-1}. A trace of detergent spreads over the pond and lowers the surface tension to γ=0.040\gamma = 0.040 N m−1^{-1}; the density stays at ρ=1000\rho = 1000 kg m−3^{-3}. Take g=9.8g = 9.8 m s−2^{-2} and treat the water as deep, inviscid and incompressible, with small-amplitude waves so that ω2=gk+γk3/ρ\omega^{2} = gk + \gamma k^{3}/\rho. ((a)) For the clean water, find the minimum phase speed and the wavelength at which it occurs. ((b)) Repeat for the contaminated water. ((c)) State how the minimum phase speed scales with γ\gamma at fixed ρ\rho and gg, and give the percentage by which the detergent reduces it.

Browse the problem library