The intensity of an earthquake wave passing through the Earth is measured to be 1.5×10^6 J/m^2*s at a distance of 58km 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 ?
To find the intensity of the earthquake wave when it 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 decreases with the square of the distance from the source.
The equation for the inverse square law is:
I2 = I1 × (d1^2 / d2^2)
where I2 is the intensity at the new distance, I1 is the initial intensity, d1 is the initial distance, and d2 is the new distance.
Given:
I1 = 1.5×10^6 J/m^2*s (initial intensity)
d1 = 58 km = 58000 m (initial distance)
d2 = 2.0 km = 2000 m (new distance)
Plugging in these values into the inverse square law equation:
I2 = 1.5×10^6 J/m^2*s × (58000 m^2 / 2000 m^2)
Calculating this equation will give you the intensity of the earthquake wave when it passed a point only 2.0 km from the source.
To find the rate at which energy passed through an area of 3.0 m^2 at 2.0 km, we can use the intensity formula:
I = P/A
where I is the intensity, P is the power, and A is the area.
Given:
I = (result from previous calculation) J/m^2*s (intensity at 2.0 km)
A = 3.0 m^2 (area)
d = 2.0 km = 2000 m (distance)
We can rearrange the formula to solve for power:
P = I × A
Plugging in the given values, we can calculate the rate at which energy passed through an area of 3.0 m^2 at 2.0 km.