The intensity of a particular earthquake wave is measured to be 5.0 multiplied by 106 J/m2·s at a distance of 55 km from the source.
(a) What was the intensity when it passed a point only 3.0 km from the source?
(b) What was the rate energy passed through an area of 7.0 m2 at 3.0 km?
Earthquake wave attenuation depends upon the wave type. They are also attenuated by heating. Some propagate along the surface and some do not go through water. The intensity does not in general follow an inverse square law reduction in intensity.
This is an ill-advised question, but they probably want you to assume that intensity varies with the inverse square of distance. To do that, multiply
5*10^6 W/m^2 by (55/3)^2
To answer these questions, we can use the inverse square law, which states that the intensity of a wave decreases with the square of the distance. The formula for the intensity with respect to distance is:
I2 / I1 = (r1 / r2)²
Where:
- I1 is the initial intensity
- I2 is the final intensity
- r1 is the initial distance
- r2 is the final distance
Let's solve each question step by step:
(a) What was the intensity when it passed a point only 3.0 km from the source?
We are given:
- Initial intensity (I1) is 5.0 x 10^6 J/m².s
- Initial distance (r1) is 55 km (or 55,000 m)
- Final distance (r2) is 3 km (or 3,000 m)
Substituting the values into the inverse square law formula, we get:
I2 / (5.0 x 10^6 J/m².s) = (55,000 m / 3,000 m)²
Simplifying the equation:
I2 / (5.0 x 10^6 J/m².s) = (18.33)²
I2 = (5.0 x 10^6 J/m².s) * (18.33)²
Calculating the value:
I2 = 1.659 x 10^9 J/m².s
Therefore, the intensity when it passed a point only 3.0 km from the source is approximately 1.659 x 10^9 J/m².s.
(b) What was the rate energy passed through an area of 7.0 m² at 3.0 km?
To calculate the rate of energy passing through an area, we can multiply the intensity by the area. We are given:
- Intensity (I) is 1.659 x 10^9 J/m².s
- Area (A) is 7.0 m²
The rate of energy passing through the area (P) can be calculated as:
P = I * A
P = (1.659 x 10^9 J/m².s) * (7.0 m²)
Calculating the value:
P = 1.1613 x 10^10 J/s
Therefore, the rate of energy passing through an area of 7.0 m² at 3.0 km is approximately 1.1613 x 10^10 J/s.