The intensity of an earthquake wave passing through the Earth is measured to be 2.5×10^6 J/m^2 at a distance of 43 km from the source. What was its intensity when it passed a point only 2.0 km from the source? AND At what rate did energy pass through an area of 4.0 m^2 at 2.0 km? Really need help with this problem please!!!
Use the inverse square law. "intensity" is the total energy in the seismic wave per unit area.
2 km is 43/2 = 21.5 times closer than 43 km. Intensity will increase by a factor 21.5^2 = 462. (That's where the inverse-square law comes in). The intensity at 2 km is therefore 1.15*10^9 J/m^2. Multiply that by 4 m^2 for the total energy through that area. That will be a lot of energy. Billions of Joules would probably destroy any building located there
Oh, earthquakes, those wild parties Earth throws every now and then! Let's see if I can entertain you with some answers.
To find the intensity when the wave passed a point only 2.0 km from the source, we can use the inverse square law. The intensity of the wave is inversely proportional to the square of the distance from the source.
So, if the intensity at 43 km is 2.5×10^6 J/m^2, we can use the equation:
Intensity at 2 km = (Intensity at 43 km) × (Distance at 43 km)^2 / (Distance at 2 km)^2
Plug in the values:
Intensity at 2 km = (2.5×10^6 J/m^2) × (43 km)^2 / (2 km)^2
Now, grab your calculator and let's crunch some numbers! Or you can pretend to be a calculator and make beep-boop noises while pretending to crunch.
For the second part, let's calculate the rate at which energy passed through an area of 4.0 m^2 at 2.0 km. To do this, we use the formula:
Energy Flux = Intensity × Area
So, in this case, the energy flux would be:
Energy Flux = Intensity at 2 km × 4.0 m^2
Again, go ahead and crunch those numbers or beep and boop if that's your thing.
I hope this helps, or at least brings a smile to your face in the midst of earthquake calculations!
To find the intensity of the earthquake wave at a point 2.0 km from the source, we can use the inverse square law of intensity, which states that the intensity is inversely proportional to the square of the distance from the source.
Given:
Intensity at 43 km = 2.5×10^6 J/m^2
Using the inverse square law, we can set up the following formula:
Intensity at 43 km / Intensity at 2.0 km = (Distance at 2.0 km)^2 / (Distance at 43 km)^2
Let's solve for the intensity at 2.0 km:
Intensity at 2.0 km = (Intensity at 43 km * (Distance at 2.0 km)^2) / (Distance at 43 km)^2
Substituting the given values, we have:
Intensity at 2.0 km = (2.5×10^6 J/m^2 * (2.0 km)^2) / (43 km)^2
Calculating this, we get:
Intensity at 2.0 km = 9.82×10^3 J/m^2
So, the intensity of the earthquake wave at a point 2.0 km from the source is 9.82×10^3 J/m^2.
Now, let's calculate the rate at which energy passes through an area of 4.0 m^2 at 2.0 km.
Given:
Area = 4.0 m^2
Distance = 2.0 km
To find the rate at which energy passes through the area, we can use the formula:
Rate = Intensity * Area
Plugging in the values, we have:
Rate = (9.82×10^3 J/m^2) * (4.0 m^2)
Calculating this, we get:
Rate = 3.93×10^4 J/s
So, the rate at which energy passes through an area of 4.0 m^2 at 2.0 km is 3.93×10^4 J/s.
To find the intensity of the earthquake wave when it passed a point 2.0 km from the source, we can use the inverse square law. This law states that the intensity of a wave is inversely proportional to the square of the distance from the source.
First, let's find the relative distance between the two points:
Relative distance = (distance at point 2.0 km) / (distance at point 43 km)
Relative distance = 2.0 km / 43 km
Next, let's find the intensity at the closer point:
Intensity at point 2.0 km = (Intensity at point 43 km) / (Relative distance^2)
Intensity at point 2.0 km = (2.5×10^6 J/m^2) / (2.0 km / 43 km)^2
Simplifying:
Intensity at point 2.0 km = (2.5×10^6 J/m^2) / (0.0465)^2
Intensity at point 2.0 km ≈ 1.33×10^9 J/m^2
Therefore, the intensity of the earthquake wave when it passed a point 2.0 km from the source is approximately 1.33×10^9 J/m^2.
Now, let's find the rate at which energy passed through an area of 4.0 m^2 at 2.0 km.
Energy Flux = Intensity × Area
Energy Flux = (1.33×10^9 J/m^2) × (4.0 m^2)
Energy Flux = 5.32×10^9 J
Therefore, the rate at which energy passed through an area of 4.0 m^2 at 2.0 km is approximately 5.32×10^9 J.