If one earthquake is 160 times as intense as another, how much larger is its magnitude on the Richter scale? (Round your answer to one decimal place.)
log 160 = 2.2
Well, if we're talking about earthquakes, we're in shaky territory! The Richter scale is a logarithmic scale, so things can get a little wobbly when it comes to figuring out the difference in magnitudes. If one earthquake is 160 times as intense as another, we can use some mathematical magic to find the answer. Since the Richter scale increases by approximately one unit for every tenfold increase in amplitude, an increase in intensity by a factor of 160 is roughly equivalent to an increase in magnitude by about 2.7. But hey, numbers can be a bit slippery, so let's round it to one decimal place... *drumroll*... we're looking at an increase in magnitude of approximately 2.7 on the Richter scale.
The Richter scale is logarithmic, meaning that each whole number increase represents a tenfold increase in the amplitude of the seismic waves.
To determine the magnitude difference between two earthquakes that are 160 times as intense, we need to calculate the logarithm base 10 of 160.
Log(160) = 2.2
Therefore, the magnitude on the Richter scale would be approximately 2.2 higher for an earthquake 160 times as intense.
To determine the difference in magnitude on the Richter scale, we can use the formula:
ΔM = log10(E2/E1)
Where ΔM is the difference in magnitude, E2 is the intensity of the second earthquake, and E1 is the intensity of the first earthquake.
In this case, it is given that one earthquake is 160 times as intense as another. Let's assume the intensity of the first earthquake (E1) is 1 unit. Therefore, the intensity of the second earthquake (E2) would be 160 units.
Now we substitute these values into the formula:
ΔM = log10(160/1)
To solve this equation, we can take the logarithm of both sides:
ΔM = log10(160) - log10(1)
Since log10(1) is equal to zero, the equation simplifies to:
ΔM = log10(160)
Using a calculator, we can evaluate log10(160) which is approximately 2.2041.
Therefore, the difference in magnitude on the Richter scale is approximately 2.2.