A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.8 multiplied by 102 µm. Find this earthquake's magnitude on the Richter scale. (Round your answer to the nearest tenth.)
M =
M=6.8
6.8 is correct! Thank You!
We all know an answer is worth nothing without an explanation. instead of 5.6 I have 5.8 but I have no clue what you did, so thanks....for nothing
To find the earthquake's magnitude on the Richter scale, we need to use the formula:
M = log(A) + log(D) - 3.0
Where:
M is the magnitude on the Richter scale
A is the maximum amplitude of the earthquake's waves in µm
D is the epicentral distance in kilometers
In this case, the maximum amplitude A is given as 5.8 multiplied by 10^2 µm and the epicentral distance D is 300 km.
First, let's convert the amplitude to the standard unit (meters) by dividing it by 10^6:
A = 5.8 x 10^2 µm = 5.8 x 10^2 / 10^6 = 5.8 x 10^-4 m
Next, we can substitute the values into the formula:
M = log(5.8 x 10^-4) + log(300) - 3.0
Using a scientific calculator, or an online logarithm calculator, we can calculate the logarithms:
log(5.8 x 10^-4) ≈ -3.7642
log(300) ≈ 2.4771
Now, substitute the calculated logarithms into the formula:
M = -3.7642 + 2.4771 - 3.0
Simplifying the equation:
M = -4.2871
Rounding the answer to the nearest tenth:
M ≈ -4.3
Therefore, the earthquake's magnitude on the Richter scale is approximately -4.3.