Final answer:
To calculate the intensity of an earthquake wave at 1 km from the source when given the intensity at 50 km, we use the inverse square law. The intensity increases as the distance decreases, so at 1 km, the intensity is 6.25×10⁹ J/m²·s.
Step-by-step explanation:
The question is asking to calculate the intensity of an earthquake wave at a different point than the given measurement, specifically at a closer distance to the source. To find the intensity at 1.0 km from the source, we can use the inverse square law, which states that intensity is inversely proportional to the square of the distance from the source. Since the original intensity is given at 50 km, we can set up a ratio using the distances and solve for the new intensity at 1.0 km.
Using the formula I1/I2 = D2²/D1² (where I1 is the original intensity, I2 is the new intensity, D1 is the original distance, and D2 is the new distance), we can substitute the known values: (2.5×10⁶ J/m²·s)/I2 = (50 km)²/(1.0 km)². Simplifying the equation, we find that I2 equals (2.5×10⁶ J/m²·s) × (50²). The new intensity at 1.0 km from the source will be 6.25×10⁹ J/m²·s.