Richter Scale

Definition

The Richter Scale measures the magnitude of earthquakes using a logarithmic scale. Each whole number increase on the scale represents a tenfold increase in measured amplitude and roughly 31.6 times more energy release.

5 Must Know Facts For Your Next Test

1. The Richter Scale is logarithmic, meaning each unit increase corresponds to a tenfold increase in earthquake amplitude.
2. A magnitude 5 earthquake releases approximately 31.6 times more energy than a magnitude 4 earthquake.
3. The formula for calculating the magnitude $M$ on the Richter Scale is $M = \log_{10}(A/A_0)$ where $A$ is the amplitude of seismic waves and $A_0$ is a reference amplitude.
4. Logarithmic functions are used to model phenomena that span several orders of magnitude, such as earthquakes on the Richter Scale.
5. Understanding properties of logarithms, like product, quotient, and power rules, helps in comprehending how magnitudes on the Richter Scale are calculated.

Review Questions

• How does an increase from magnitude 4 to magnitude 5 on the Richter Scale affect the measured amplitude and energy release?
• What is the logarithmic formula used to calculate earthquake magnitudes on the Richter Scale?
• Why are logarithmic functions suitable for measuring earthquake magnitudes?

Related terms

Logarithm: A mathematical function that determines how many times one number must be multiplied by itself to reach another number.

$\log_{10}$: The common logarithm with base 10, often used in scientific measurements including the Richter Scale.

$e^{x}$ (Exponential Function): A mathematical function denoting exponential growth or decay, inverse to logarithmic functions.