(II) What is the ratio of (a) the intensities, and (b) the...

(II) What is the ratio of $(a)$ the intensities, and $(b)$ the amplitudes, of an earthquake P wave passing through the Earth and detected at two points $15 \mathrm{~km}$ and $45 \mathrm{~km}$ from the source.

Key Concepts

Amplitude-Intensity Relationship

There is a direct mathematical connection between the amplitude of a wave and its intensity. Specifically, the intensity of a wave is proportional to the square of its amplitude (I ? A²). This relationship implies that when the intensity of a wave is reduced by geometrical spreading (as described by the inverse square law), the amplitude decreases by the square root of the intensity reduction. Understanding this relationship is crucial when comparing the amplitudes recorded at different distances from the wave's source.

Inverse Square Law for Intensities

The inverse square law is a key concept in understanding how the intensity of waves decreases with distance. For a point source radiating energy uniformly in all directions, the intensity of the wave at a given distance is inversely proportional to the square of that distance. This relationship explains how the energy per unit area (intensity) diminishes as the wavefront expands over a larger spherical surface.

Seismic Wave Propagation

Seismic waves, such as earthquake P waves, propagate energy from the source through the Earth. As these waves travel outward, the energy is spread over an increasingly larger area, typically in three dimensions. This dispersion of energy with distance is a fundamental aspect of wave behavior in seismology and allows us to analyze the attenuation of the waves as they move away from the source.

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