Liquid mercury at room temperature has surface tension and density

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

Modes, Packets and Media, Ch Water waves and de Broglie waves

Problem

Liquid mercury at room temperature has surface tension σ=0.487 N m−1\sigma = 0.487\,\mathrm{N\,m^{-1}} and density ρ=13534 kg m−3\rho = 13534\,\mathrm{kg\,m^{-3}}. Take g=9.8 m s−2g = 9.8\,\mathrm{m\,s^{-2}} and assume an unbounded, deep pool so that only the gravity-capillary dispersion relation ω2=gk+σk3/ρ\omega^2 = gk + \sigma k^3/\rho applies. ((a)) Find the minimum possible phase speed of surface waves on mercury. ((b)) Find the wavelength at which this minimum occurs.

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