An earthquake in California measured 4.9 on the Richter scale. Use the formula R=log(A/A_0) to determine approximately how many times stronger the wave amplitude A of the earthquake was than A_0.

The formula for the Richter scale is given by:

\[
R = \log\left(\frac{A}{A_0}\right)
\]

Where:
- \( R \) is the Richter scale measurement (4.9 in this case),
- \( A \) is the wave amplitude of the earthquake,
- \( A_0 \) is the reference amplitude.

To find how many times stronger the wave amplitude \( A \) is compared to \( A_0 \), we solve for the ratio \( \frac{A}{A_0} \).

Given:
\[
R = 4.9
\]

Substitute into the formula:

\[
4.9 = \log\left(\frac{A}{A_0}\right)
\]

Now, solve for \( \frac{A}{A_0} \) by exponentiating both sides of the equation to base 10:

\[
\frac{A}{A_0} = 10^{4.9}
\]

Let's compute \( 10^{4.9} \).

\[
\frac{A}{A_0} \approx 10^{4.9} \approx 7943.28
\]

Therefore, the wave amplitude \( A \) of the earthquake was approximately **7,943 times stronger** than the reference amplitude \( A_0 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the physical meaning of the reference amplitude \( A_0 \)?
2. How does the Richter scale compare to other earthquake magnitude scales?
3. How is the energy released by an earthquake related to the Richter scale measurement?
4. What is the difference between wave amplitude and energy released during an earthquake?
5. How do different Richter scale values affect building structures?

**Tip:** A small change in the Richter scale value corresponds to a significant change in amplitude and energy released by an earthquake.

An earthquake in California measured 4.9 on the Richter scale. Use the formula R = log(A/A_0) to determine approximately how many times stronger the wave amplitude A of the earthquake was than A_0.

Learn how to calculate the wave amplitude of an earthquake using the Richter scale formula R = log(A/A_0). This example uses an earthquake with a magnitude of 4.9 to demonstrate how logarithmic relationships help determine the amplitude ratio. Suitable for Grades 10-12.

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