(II) The intensity of an earthquake wave passing through the...

(II) The intensity of an earthquake wave passing through the Earth is measured to be $3.0 \times 10^{6} \mathrm{J} / \mathrm{m}^{2} \cdot \mathrm{s}$ at a distance of 48 $\mathrm{km}$ from the source. (a) What was its intensity when it passed a point only 1.0 $\mathrm{km}$ from the source? (b) At what rate did energy pass through an area of 2.0 $\mathrm{m}^{2}$ at 1.0 $\mathrm{km}$ ?

(II) The intensity of an earthquake wave passing through the Earth is measured to be $3.0 \times 10^{6} \mathrm{J} / \mathrm{m}^{2} \cdot \mathrm{s}$ at a distance of 48 $\mathrm{km}$ from the source. (a) What was its intensity when it passed a point only 1.0 $\mathrm{km}$ from the source?
(b) At what rate did energy pass through an area of 2.0 $\mathrm{m}^{2}$ at 1.0 $\mathrm{km}$ ?

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Key Concepts

Energy Flux

Energy flux refers to the rate at which energy passes through a given area. It is an important concept in determining how much energy is being transferred in a system, and it is directly related to intensity, representing the energy flow per unit area per unit time.

Inverse Square Law

The inverse square law describes how the intensity of a wave radiating from a point source decreases in proportion to the square of the distance from the source. This is due to the energy spreading out over the surface of a sphere whose area increases with the square of the radius, leading to lower energy per unit area at greater distances.

Intensity

Intensity is a measure of the energy transmitted by a wave per unit area per unit time as it moves through a medium. It quantifies how much energy is being delivered to a specific area over a specified time interval, and is a critical concept when analyzing wave phenomena, including seismic waves, sound waves, and electromagnetic waves.

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