Consider deep-water gravity waves of short enough wavelength that surface tension must be included, so the dispersion relation is Eq. (16.14). Show that there is a minimum value of the group velocity, and find its value together with the wavelength of the associated wave. Evaluate these for water (γ ∼ 0.07 N m⁻¹= 70 dyne/cm). Try performing a crude experiment to verify this phenomenon.

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2 w² = gk + Yk³ P (16.14)