Question

The intensity of an earthquake wave passing through the Earth is measured to be 2.5 X 10⁶J/m² s at a distance of 42 km from the source. What was its intensity when it passed a point only 1.5 km from the source?

Answer 1

The intensity of the earthquake wave at 1.5 km from the source is calculated using the inverse square law and is found to be 1.96 X 10¹ J/m² s when the known intensity at 42 km is 2.5 X 10⁶ J/m² s.

Step-by-step explanation:

The question is asking how the intensity of an earthquake wave changes as it travels through the Earth and covers different distances. To find the intensity of the earthquake wave at a point 1.5 km from the source when the intensity at a distance of 42 km is known to be 2.5 X 106J/m2 s, we must understand that the intensity of waves like earthquake waves follows an inverse square law. This means that the intensity is inversely proportional to the square of the distance from the source.

The formula for this relationship is:

I1 / I2 = (D2 / D1)2

Where I1 is the intensity at distance D1, and I2 is the intensity at distance D2. Now we can plug in the values to find the initial intensity:

I1 = I2 * (D2 / D1)2

I1 = 2.5 X 106 J/m2 s * (42,000 m / 1,500 m)2

I1 = 2.5 X 106 J/m2 s * (282)

I1 = 2.5 X 106 J/m2 s * 784
I1 = 1.96 X 109 J/m2 s