## Sunday, June 28, 2015

### The Richter scale: From two readings, the relative strength and vice versa

In class last week, we learned how to find out how much stronger one quake is compared to another given the two Richter scale readings. For example, on June 28, the strongest quake in the U.S. was a 3.4 in Oklahoma, while the strongest in North America was a 5.4 in Niltepec, Mexico. What is the difference in levels of energy? Here are the steps.

Step 1: Subtract little from big. In our case, 5.4 - 3.4 = 2.0.
Step 2: multiply difference by 1.5. 2.0 * 1.5 = 3.0.
Step 3: Raise 10 to the power of the answer from Step 2: 10^3.0 = 1,000. The Mexican quake was 1,000 times stronger than the Oklahoma quake.

Let's ask the question in the opposite direction. Let's say we have a reading for a quake and we know another quake was x times stronger. Again, it will be a three step process, but now we will take the inverse of our three steps above in reverse order. Let's say we have a quake 350 times stronger than the one in Niltepec.  Here are our steps.

Step 1: Take the log of the strength multiplier. Log is the inverse of raising 10 to a power, just like addition is the inverse of subtraction and division is the inverse of multiplication. log(350) = 2.544...,
Step 2: divide the answer from Step 1 by 1.5 and round this answer to the nearest tenth. 2.544/1.5 = 1.696..., which rounds to 1.7. We round to the nearest tenth because the Richter scale rounds to the nearest tenth.
Step 3: Add the answer from Step 2 to the Richter reading we know. In this case, it would be 5.4+1.7 = 7.1, the reading of the stronger quake. If instead we were told a quake was 350 times weaker than Niltepec, it would be 5.4-1.7 = 3.7

1. 16 times stronger than a 6.1
2. 250 times stronger than a 6.7
3. 8 times weaker than a 5.8

#### 1 comment:

Prof. Hubbard said...

1. 16 times stronger than a 6.1

Step 1: Log 16 = 1.204...
Step 2: 1.204/1.5 = 0.802..., which rounds to 0.8
Step 3: 6.1 + 0.8 = 6.9

2. 250 times stronger than a 6.7

Step 1: Log 250 = 2.3979
Step 2: 2.3979/1.5 = 1.5986..., which rounds to 1.6
Step 3: 6.7 + 1.6 = 8.3

3. 8 times weaker than a 5.8

Step 1: Log 8 = 0.903
Step 2: 0.903/1.5 = 0.602..., which rounds to 0.6
Step 3: 5.8 - 0.6 = 5.2

In Step 3 of the third problem, we subtracted instead of adding because the quake was weaker.