The Richter scale formula is expressed as:
\[ R = \log\left(\frac{A}{A_0}\right) \]
where:
- \( R \) is the magnitude of the earthquake on the Richter scale,
- \( A \) is the amplitude of the earthquake wave,
- \( A_0 \) is a reference amplitude.
Given that the earthquake measured \( R = 51.1 \), we can rearrange the formula to solve for the ratio \(\frac{A}{A_0}\):
\[ R = \log\left(\frac{A}{A_0}\right) \implies \frac{A}{A_0} = 10^R \]
Now, substituting \( R = 51.1 \):
\[ \frac{A}{A_0} = 10^{51.1} \]
Now we calculate \( 10^{51.1} \):
\[ 10^{51.1} \approx 1.2589 \times 10^{51} \]
This means the amplitude \( A \) of the earthquake wave was approximately \( 1.2589 \times 10^{51} \) times stronger than the reference amplitude \( A_0 \).
So, the wave amplitude of the earthquake was approximately \( 1.26 \times 10^{51} \) times stronger than the reference amplitude.
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