Suppose one earthquake measures 9.5 on the Richter scale and another measures 8.7 on the Richter scale. How much more intense was the first earthquake than the second earthquake? Round to the nearest whole number.
Question
Suppose one earthquake measures 9.5 on the Richter scale and another measures 8.7 on the Richter scale. How much more intense was the first earthquake than the second earthquake? Round to the nearest whole number.
Solution
The Richter scale is a logarithmic scale, which means that each whole number increase on the scale represents a tenfold increase in measured amplitude and roughly 31.6 times more energy release.
To find out how much more intense the first earthquake was than the second, you subtract the Richter scale measurement of the second earthquake from that of the first.
9.5 - 8.7 = 0.8
This means that the first earthquake was 0.8 units higher on the Richter scale than the second earthquake.
Because the Richter scale is logarithmic, you can't simply say that the first earthquake was 0.8 times more intense than the second. Instead, you have to use the fact that each unit on the Richter scale represents a tenfold increase in amplitude and a 31.6-fold increase in energy release.
So, to find out how much more intense the first earthquake was than the second, you raise 10 (the base of the logarithm) to the power of the difference in Richter scale measurements.
10^0.8 = 6.31
So, the first earthquake was roughly 6 times more intense than the second earthquake when considering the amplitude of the seismic waves.
However, if we consider the energy release, we have to raise 31.6 to the power of the difference in Richter scale measurements.
31.6^0.8 = 15.85
So, the first earthquake released roughly 16 times more energy than the second earthquake.
Therefore, depending on whether you're considering the amplitude of the seismic waves or the energy release, the first earthquake was either 6 or 16 times more intense than the second.
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