Two coastal recorders on the same great circle from a distant storm plot the…

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Waves in two and three dimensions, dispersion and wave packets · Waves in two and three dimensions, dispersion and wave packets

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

Problem

Two coastal recorders on the same great circle from a distant storm plot the frequency of arriving deep-water swell against time

t

since a common reference clock,

t=0

. Each plot is a straight line. Station 1's line passes through the points

(t,f) = (2.0\,\mathrm{d},\,0.0400\,\mathrm{Hz})

and

(6.0\,\mathrm{d},\,0.0600\,\mathrm{Hz})

. Station 2's line passes through

(3.0\,\mathrm{d},\,0.0337\,\mathrm{Hz})

and

(9.0\,\mathrm{d},\,0.0562\,\mathrm{Hz})

. ((a)) Find the storm's distance from each station. ((b)) Find the time, relative to

t=0

, at which the storm occurred, from each station's line, and check that the two agree.

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