Question

The amplitude recorded at a station for a magnitude 5 earthquake is 𝑥. If another earthquake recorded at the same station has an amplitude of 15𝑥, then the magnitude of this earthquake is ________. (Round off to two decimal places)

Answer 1

Correct Answer: 6.1

Given:
Magnitude of first earthquake: \(M_1 = 5\)
Amplitude at station: \(A_1 = x\)
Amplitude of second earthquake: \(A_2 = 15x\) 
We need \(M_2\). 
Step 1 — Use Richter magnitude formula:
\[ M = \log_{10}\frac{A}{A_0} \] where \(A_0\) is a reference amplitude (same for both, so it cancels in difference). Difference in magnitude: \[ M_2 - M_1 = \log_{10}\frac{A_2}{A_1} \] 
Step 2 — Plug in values:
\[ M_2 - 5 = \log_{10}\frac{15x}{x} = \log_{10}15 \] \[ \log_{10} 15 \approx 1.1761 \] \[ M_2 = 5 + 1.1761 \approx 6.18 \] Answer (rounded to two decimals): \(\boxed{6.18}\)