Question 1126122: A certain city has recently experienced an earthquake that contained a magnitude of 5.9. Compare its intensity with the intensity of an earthquake at zero-level.
There are choices but I don't really know how to solve it. Please help. Thanks!
A.
The intensity of the earthquake at the city was approximately 683,217.55 times the intensity of a zero-level earthquake.
B.
The intensity of the earthquake at the city was approximately 794,328.23 times the intensity of a zero-level earthquake.
C.
The intensity of the earthquake at the city was approximately 619,504.91 times the intensity of a zero-level earthquake.
D.
The intensity of the earthquake at the city was approximately 704,594.86 times the intensity of a zero-level earthquake.
E.
The intensity of the earthquake at the city was approximately 803,116.72 times the intensity of a zero-level earthquake.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the magnitude of an earthquake at 0 level would be 10^0.
the magnitude of an earthquake at 5.9 level would be 10^5.9
10^5.9 / 10^0 = 10^5.9 = 794328.2347.
round that to 794328.23 and you get selection B.
what this says is that a magnitude 5.9 earthquake is 794328.2347 times as powerful as a magnitude 0 earthwuake.
this assumes the richter scale is used to find the magnitude of an earthquake.
each unit on the richter scale is 10 times the previous unit.
a good reference about the richter scale can be found here:
http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U18_L4_T2_text_container.html
using this reference, your formula would becomes:
5.9 = log(x * A0 / A0) which would becomes 5.9 = log(x).
this is true if and only if 10^5.9 = x.
this results in x = 10^5.9 = 794328.2347 which rounds to 794328.23.
this translates to a magnitude 5.9 earthquake being 794328.23 times as powerful as a magnitude 0 earthquake based on how i understand it.
since the richter scale measures the magnitude of the earthwuake as its souce, and the measurements are rarely done right at the source, then there are some adjustments made based on the distance of the measurement from the source to come up with the assumed measurement at the source.
also, the intensity of the earthquake takes into account other factors besides the magnitude that go into the effect of the earthquake.
in other words, the real world measurements are more complex and take into account factors other than what you see on the richter scale.
some additional references you might find interesting are:
https://courses.lumenlearning.com/geo/chapter/reading-magnitude-versus-intensity/
http://www.odec.ca/projects/2008/liya8y2/magnitude.html
for your problem, i believe they were referencing the richter scale measurements only.
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