A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.5 102 µm. Find this earthquake's magnitude on the Richter scale. (Round your answer to the nearest tenth.)
To find the earthquake's magnitude on the Richter scale, we need to use the formula:
Magnitude = log(A/A0)
Where A is the amplitude of the earthquake measured on the seismograph, and A0 is a reference amplitude of 1 µm.
In this case, the amplitude recorded on the seismograph is 5.5 × 10^2 µm.
So, we can calculate the magnitude using the formula:
Magnitude = log(5.5 × 10^2/1)
To evaluate this calculation, we can use the logarithm properties. Since the base of the logarithm is not specified, we can assume it is base 10.
Magnitude = log10(5.5 × 10^2) - log10(1)
Magnitude = log10(550) - log10(1)
Now we can use a calculator to find the log values:
Magnitude ≈ 2.74 - 0
Magnitude ≈ 2.74
Therefore, the earthquake's magnitude on the Richter scale is approximately 2.7 (rounded to the nearest tenth).