A stone dropped into a lake much deeper than any wavelength considered generates…

PHYSICS · Subjective · Fermi University Physics · Oscillations, Waves & Acoustics · Fluids & Continuum Physics · Waves, acoustics and compressible flow

Modes, Packets and Media, Ch Dispersion and the propagation of wave packets

Problem

A stone dropped into a lake much deeper than any wavelength considered generates ripples obeying the deep-water dispersion relation

\omega = \sqrt{gk}

, with

g = 9.8\,\mathrm{m\,s^{-2}}

. A float sits

x = 8.0\,\mathrm{m}

from the point of impact. Using stationary phase, for which the stationary wavenumber satisfies

\omega'(k_{\rm s}) = x/t

, find the wavelength the float sees at

t = 15\,\mathrm{s}

after the stone lands.

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