Question

The intensity of an earthquake wave passing through the Earth is measured to be 3.0 X 10⁶ J/m² s at a distance of 54 km from the source.

(a) What was its intensity when it passed a point only 1.0 km from the source?

(b) At what rate did energy pass through an area of 2.0m² at 1.0 km?

 

Answer 1

Concepts and reason

The concepts used to solve this problem are the relation between the distance and the intensity of earth quake wave, and the relation between rate of energy that passes and the intensity of the earth quake wave.

First, use the relation between the distance and the intensity of the earth quake wave to find the intensity of the earth quake wave at a distance from the source point.

Then, use the relation between rate of energy that passes and the intensity of the earth quake wave to find the rate of energy that passes through an area of at a distance of from the source position.

Fundamentals

The expression that relates the distance and intensity of the earth quake wave is as follows:

Here, the intensity at a distance from the source is and the intensity of the source is .

The expression that relates the rate of energy that passes and intensity of the earth quake wave is given by the relation as follows:

Here, the energy is and the area through which the energy passes is .

(a)

The expression that relates the distance and intensity of the earth quake wave is as follows:

Let the intensity at a distance be and the intensity at a distance be .

Therefore, the expression of intensities and are as follows:

Now, take the ratio .

Rearrange to get .

Substitute for , for , and for to find the intensity at a distance from the source.

(b)

The expression that relates the rate of energy that passes and the intensity of the earth quake wave is given by the relation as follows:

Substitute for and for in the above expression to find the rate of energy that passes through the area of at a distance of .

Ans: Part a

The intensity at a distance from the source is .

Part b

The rate of energy that passes through the area of at distance is .