A seismograph 300km from the epicenter of an earthquake recorded a maximum amplitude of 5.8*10^2lrm, find this earthquake's magnitude on the RicHTER scale to the nearest tenth.
To determine the magnitude of an earthquake on the Richter scale, you'll need the maximum amplitude recorded by a seismograph, as well as the distance between the seismograph and the earthquake's epicenter. In this case, we have the maximum amplitude of 5.8 * 10^2, but we need the distance.
Given that the seismograph is 300 km from the epicenter, we can use this information to calculate the magnitude on the Richter scale using the following formula:
M = log(A / A0)
where:
M = Magnitude on the Richter scale
A = Maximum amplitude recorded by the seismograph
A0 = Reference amplitude at a standard distance of 100 km
First, we need to calculate the reference amplitude (A0) at a standard distance. Using the equation:
log(A / A0) = (log A) - (log A0)
We can rearrange the equation to solve for A0:
A0 = A / 10^(log A / log 10)
Now, let's substitute the given values into the equation:
A = 5.8 * 10^2
Distance = 100 km (a standard distance)
A0 = 5.8 * 10^2 / 10^(log (5.8 * 10^2) / log 10)
Using a calculator, calculate log (5.8 * 10^2) ÷ log 10, which should give you approximately 2.76:
A0 = 5.8 * 10^2 / 10^2.76
Now, calculate 10^2.76 on the calculator, which should give you approximately 503.97:
A0 = 5.8 * 10^2 / 503.97
Next, divide the maximum amplitude (A) by the reference amplitude (A0) to find the magnitude (M):
M = log(A / A0)
Substitute the values:
M = log(5.8 * 10^2 / 503.97)
Using a calculator, calculate 5.8 * 10^2 / 503.97, which should give you approximately 1.152:
M = log(1.152)
Finally, calculate the logarithm base 10 of 1.152 on the calculator, which should give you approximately 0.061:
M = 0.061
Therefore, the magnitude of the earthquake on the Richter scale is approximately 0.1 when rounded to the nearest tenth.