Two offshore tsunami monitoring buoys record the amplitude of a wave trig- gered

Question

Two offshore tsunami monitoring buoys record the amplitude of a wave trig- gered by an earthquake that was not close to any land. The buoys are 20 km and 120 km away from the epicentre of the quake. The buoy 20km away records a tsunami wave 0.5m high. (a) How does the power per metre contained in the wave depend on the amplitude (height) of the wave? (note: this is an intensity for a 2-dimensional surface) (b) How does the power per metre depend on distance from the source? (c) What height of wave do you expect the second buoy to record? (d) In reality, the second buoy records a wave height of 0.19m. What fraction of the energy in the wave has been dissipated (lost) in the time the wave travelled from the first buoy to the second?

Explanation / Answer

I=P/A=P/d^2=a^2

where I=intensity

P=power

A=area

a=amplitude

a)intensity is proportional to the square of the amplitude

b) intensity is inversly proportional to the square of the distance from the source

c)power of the wave is same for both the sources

so a1d1=a2d2

a2=0.5*20/120=0.083m

d)

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