Mathematics: What is the ratio of the intensities of an earthquake PP wave passing through the Earth and detected at two points 19 kmkm and 46 kmkm from the source?

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What is the ratio of the intensities of an earthquake

harri26348

18.01.2022

The ratio of the intensities is roughly 6:1.

Step-by-step explanation:

The intensity I() of an earthquake wave is given by:

$I = \frac{P}{4\pi d^{2}}$

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:

$\frac{I_{1}}{I_{2}} = \frac{P/4\pi d_{1}^{2}}{P/4\pi d_{2}^{2}}$

where I₁ = P/4πd₁², d₁=19 km, I₁ = P/4πd₂² and d₂=46 km

$\frac{I_{1}}{I_{2}} = \frac{d_{2}^{2}}{d_{1}^{2}}$

$\frac{I_{1}}{I_{2}} = \frac{46 km^{2}}{19 km^{2}}$

$\frac{I_{1}}{I_{2}} = 5.9:1$

Therefore, the ratio of the intensities is roughly 6:1.

I hope it helps you!

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