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.
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?
1 answer
1 answer