Answer:
The ratio of the intensities is roughly 6:1.
Step-by-step explanation:
The intensity I() of an earthquake wave is given by:
[tex] I = \frac{P}{4\pi d^{2}} [/tex]
where P: is the power ans d: is the distance.
Hence, the ratio of the intensities of an earthquake wave passing through the Earth and detected at two points 19 km and 46 km from the source is:
[tex] \frac{I_{1}}{I_{2}} = \frac{P/4\pi d_{1}^{2}}{P/4\pi d_{2}^{2}} [/tex]
where I₁ = P/4πd₁², d₁=19 km, I₁ = P/4πd₂² and d₂=46 km
[tex] \frac{I_{1}}{I_{2}} = \frac{d_{2}^{2}}{d_{1}^{2}} [/tex]
[tex] \frac{I_{1}}{I_{2}} = \frac{46 km^{2}}{19 km^{2}} [/tex]
[tex] \frac{I_{1}}{I_{2}} = 5.9:1 [/tex]
Therefore, the ratio of the intensities is roughly 6:1.
I hope it helps you!
