Measuring the power of an earthquake
Here’s another example you probably won’t see in your biology class, but you’ve probably heard of it. Historically earthquakes have been compared using the Richter scale. Using this scale the magnitude of an earthquake is determined by calculating the logarithm of the amplitude of waves recorded by seismographs. Because of the logarithmic basis of the scale, each whole number increase in magnitude represents a tenfold increase in measured amplitude. (Reference: http://earthquake.usgs.gov/learn/topics/measure.php )
An earthquake hit Christchurch in New Zealand on 22 Feb 2011, measuring 6.3 on the Richter scale (tragically 185 people were killed). In 1929, an earthquake in Murchison, NZ measured 7.3, leaving 173 dead. How much greater in amplitude were the waves released in the Murchison earthquake?
In this example, the numbers on the log scale were exactly 1 unit apart, so the quick answer to how much greater the amplitude is would be simply:
101 = 10 times as much.
Likewise, if the earthquakes measured 2 and 6 on the Richter scale, that’s a difference of 4 points, and the difference in actual energy is:
104 = 10,000 times as much.
Of course the numbers on the log scale you encounter will not usually increase by exactly whole numbers of units. In the real world, measurements are messier. But the principle is the same: find the difference between the two numbers on the log scale, and calculate the anti-log of that difference.
The earthquake in Newcastle, Australia in 1989 measured 5.6 on the Richter scale. How much greater in amplitude were the waves released in the Christchurch earthquake compared to the Newcastle earthquake?