The intensity of an earthquake wave passing through the Earth is measured to be 2.5×106 J/m^2 at a distance of 48 km from the source.

What was its intensity when it passed a point only 2.0 km from the source?

At what rate did energy pass through an area of 3.0 m^2 at 2.0 km?

The intensity of an earthquake wave decreases as the square of the distance from the source. We can write this as:

I1/I2 = (D2/D1)^2

where I1 and I2 are the intensities at distances D1 and D2 from the source, respectively. We are given I1 = 2.5*10^6 J/m^2, D1 = 48 km, and D2 = 2.0 km. We want to find I2.

2.5*10^6 / I2 = (2.0 / 48)^2

Rearrange this equation to solve for I2:

I2 = 2.5*10^6 * (48 / 2.0)^2
I2 = 2.5*10^6 * (24)^2
I2 = 2.5*10^6 * 576
I2 = 1.44*10^9 J/m^2

So the intensity at a distance of 2.0 km would be 1.44*10^9 J/m^2.

To find the rate of energy passing through an area of 3.0 m^2 at 2.0 km, we can simply multiply the intensity by the area:

Rate = Intensity * Area
Rate = 1.44*10^9 J/m^2 * 3.0 m^2
Rate = 4.32*10^9 J/s

The rate at which energy passed through an area of 3.0 m^2 at 2.0 km is 4.32*10^9 J/s.

To find the intensity when the earthquake wave passed a point only 2.0 km from the source, we can use the inverse square law. According to the inverse square law, the intensity of a wave is inversely proportional to the square of the distance from the source. Mathematically, this relationship can be expressed as:

I1 / I2 = (r2^2 / r1^2)

where I1 is the initial intensity (2.5×10^6 J/m^2), I2 is the intensity at the point of interest, r1 is the initial distance (48 km converted to meters = 48,000 m), and r2 is the distance at the point of interest (2.0 km converted to meters = 2,000 m).

Plugging in the given values into the equation, we have:

I1 / I2 = (2000^2 / 48000^2)

Simplifying the equation, we find:

I2 = I1 * (r2^2 / r1^2)

Substituting the values, we get:

I2 = 2.5×10^6 J/m^2 * (2000^2 / 48000^2)

Calculating this expression gives us the intensity at a distance of 2.0 km from the source.

To determine the rate at which energy passed through an area of 3.0 m^2 at a distance of 2.0 km, we can use the formula:

Power = Intensity * Area

where Power is the rate at which energy is passing through the area, Intensity is the intensity of the wave, and Area is the given area.

Plugging in the given values, we have:

Power = Intensity * Area
Power = I2 * 3.0 m^2

Substituting the calculated value for I2 from the previous question, we can determine the rate at which energy passed through the area.