The Richter scale measure of the magnitude of the earthquake can be found by using 𝑅=log(𝐴𝐴0),where 𝐴 is the measure of the intensity of the earthquake, and 𝐴0 is the intensity of a standard earthquake (the amplitude of the smallest detectable wave).Find the magnitude of an earthquake 20% of the intensity of a magnitude 7 earthquake.Give your answer correct to one decimal place.
Question
The Richter scale measure of the magnitude of the earthquake can be found by using 𝑅=log(𝐴𝐴0),where 𝐴 is the measure of the intensity of the earthquake, and 𝐴0 is the intensity of a standard earthquake (the amplitude of the smallest detectable wave).Find the magnitude of an earthquake 20% of the intensity of a magnitude 7 earthquake.Give your answer correct to one decimal place.
Solution
First, we need to understand that the Richter scale is a logarithmic scale. This means that each whole number increase on the scale represents a tenfold increase in measured amplitude and roughly 31.6 times more energy release. A magnitude 7 earthquake is thus 10 times more intense than a magnitude 6 earthquake.
Given that, we know that a magnitude 7 earthquake is 10^7 times as intense as the smallest detectable wave (A0).
If we want to find the magnitude of an earthquake that is 20% of the intensity of a magnitude 7 earthquake, we first calculate what 20% of 10^7 is.
20% of 10^7 = 0.2 * 10^7 = 2 * 10^6
Now we can use the formula for the Richter scale to find the magnitude of this earthquake:
R = log(A/A0)
Here, A is the intensity of the earthquake we're trying to find (2 * 10^6 times as intense as A0), and A0 is the intensity of the smallest detectable wave.
So we have:
R = log(2 * 10^6)
Using the properties of logarithms, we can simplify this to:
R = log(2) + log(10^6)
R = 0.3 + 6 = 6.3
So, an earthquake that is 20% of the intensity of a magnitude 7 earthquake would be a magnitude 6.3 earthquake.
Similar Questions
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