Im confused if im doing this right
Last week there was an earthquake that measured as a magnitude of 3.2 on the Richter scale. Today you hear on the radio that there was a second earthquake that was 27 times more intense than the first. What was the magnitude of the second earthquake on the Richter scale?
Ans:to get magmitude of the second i have to multiply 27 by first earthquake which is 3.2
27(3.2)=84
But i feel there is a way more to it,and its exponetial.
No, log scale
I answered this yesterday
http://www.jiskha.com/display.cgi?id=1451681946
You multiply the 27 by the amplitude, not the log of the amplitude.
then take the log of the new bigger amplitude for the new Richter number.
here slowly
Richer number = 3.2
3.2 is log of amplitude A
log A = 3.2
10^logA = A = 10^3.2 = 10^3 * 10^.2
so A = 10^3 * 1.5848
Now Multiply THAT by your 27
B = 10^4 * 4.27921
log B = log 4 + log 4.27921
= 4.631
which is your new Richter #
Get the idea?
Richer # = log of amplitude.
so you take 27 times the antilog
and then take the log of that
Thank you so much damon!!
Well, let's put it this way. If the first earthquake was a 3.2 on the Richter scale, and the second one was 27 times more intense, I'd say the Richter scale is not messing around. It's not just a simple multiplication, it's like an exponential party!
So, let me grab my clown calculator here. If the first earthquake was a 3.2, and the second one was 27 times more intense, we need to raise 27 to the power of 3.2.
And after some clown calculations, I can tell you that the magnitude of the second earthquake on the Richter scale is approximately 144.7! Now that's what I call a shake, rattle, and roll!
You're on the right track! Calculating the magnitude of the second earthquake on the Richter scale requires some understanding of logarithms.
The Richter scale measures the amplitude (strength) of earthquakes on a logarithmic scale. This means that each increase of one unit on the Richter scale represents a tenfold increase in amplitude. In other words, an earthquake with a magnitude of 3.2 is ten times more powerful than one with a magnitude of 2.2.
To find the magnitude of the second earthquake, which is 27 times more intense than the first, we need to determine by how many units the magnitude increased. You correctly multiplied the magnitude of the first earthquake (3.2) by 27, but that doesn't directly give us the answer in terms of the Richter scale.
To convert the multiplier (27) into the equivalent increase in magnitude units, we need to take the logarithm base 10 (logarithm with base 10) of the multiplier. In this case, we want to calculate log10(27). If we round to two decimal places, log10(27) is approximately 1.43.
To find the magnitude of the second earthquake, you multiply the increase in magnitude units (1.43) by the magnitude of the first earthquake (3.2).
Using the formula:
Magnitude of the second earthquake = Magnitude of the first earthquake + log10(multiplier)
Magnitude of the second earthquake = 3.2 + 1.43 ≈ 4.63
So, the magnitude of the second earthquake on the Richter scale is approximately 4.63.