Answered: How many times more severe is the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

How many times more severe is the earthquake (R=8.3) in city A than the earthquake (R=6.5) in city C?

The earthquake in city A is approximately (blank) times more severe than the earthquake in city C.

Expert Solution

Step 1: Finding the intensity of earthquake

We know that if $R$ is the magnitude of earth quake, $I$ the intensity of the earth quake and $I_{0}$ is the intensity of the earthquake when $R$ is $0$ , then

$R = \log_{10} (\frac{I}{I_{0}}) \Rightarrow \frac{I}{I_{0}} = 10^{R} \Rightarrow I = I_{0} 10^{R}$

If the intensity of earthquake is $I_{C}$ in city $C$ and $I_{A}$ in city $A$ , $R_{C}$ is the magnitude in in city $C$ and $R_{A}$ in city $A$

Given $R_{A} = 8.3, R_{C} = 6.5$

Then;

$\Rightarrow \frac{I_{A}}{I_{C}} = \frac{10^{R_{A}}}{10^{R_{C}}} \Rightarrow \frac{I_{A}}{I_{C}} = \frac{10^{8.3}}{10^{6.5}} \Rightarrow \frac{I_{A}}{I_{C}} = 10^{8.3 - 6.5} \Rightarrow \frac{I_{A}}{I_{C}} = 10^{1.8} \Rightarrow I_{A} = 10^{1.8} I_{C}$