Resonant modes of the Earth. The seismic waves released in large earthquakes suc

Question

Resonant modes of the Earth. The seismic waves released in large earthquakes such as the 2004 Sumatra earthquake excite standing wave modes in the Earth. What are the frequencies of these standing wave modes? Let's model the Earth as a cube whose side length is equal to the Earth's diameter, and consider standing waves that exist between opposite faces of the cube. Of the two kinds of seismic waves (S and P) only the P-waves (which are longitudinal waves) will penetrate the Earth's core. Their wave speed as a function of depth is shown at right. Estimate the average P-wave speed from this plot, and then estimate the frequency of the fundamental standing wave mode. Could you hear the Earth "ringing" after a major seismic event?

Explanation / Answer

The earth ionosphere cavity is capable of supporting resonant electromagnetic modes at extremely low frequencies. The usual formula for the frequencies of these resonances is deduced from the waveguide mode theory in which propagation is essentially tangential to the earth's surface.

The average velocity of the p-wave can be estimated from the plot as by taking the minimum velocity and maximum velocity and add them. Then take the half of that sum of minima and maximum velocity. We will get the average velocity for P wave from the plot.

So minimum velocity =6 km/s

And maxumum velocity =12 km/s

Total velocity =18 km/s

Average velocity =18/2= 9 km/s

No, we cannot hear the sound after the ringing of seismic event. It is because to the fact that the range of the frequency of the seismic wave is in ultrasonic region and human ear is not Capable to hear this.

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