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Chapter 4: Problem 2

State quakes: The largest recorded earthquake centered in Idaho measured \(7.2\) on the Richter scale. a. The largest recorded earthquake centered in Montana was \(3.16\) times as powerful as the Idaho earthquake. What was the Richter scale reading for the Montana earthquake? b. The largest recorded earthquake centered in Arizona measured \(5.6\) on the Richter scale. How did the power of the Idaho quake compare with that of the Arizona quake?

Short Answer

Expert verified
Montana: 7.7 on the Richter scale. Idaho quake was 39.8 times more powerful than Arizona's quake.

Step by step solution

01

Understanding the Richter Scale

The Richter scale measures the magnitude of an earthquake. Each whole number increase on the Richter scale represents a tenfold increase in measured amplitude and approximately 31.6 times more energy release.
02

Calculate the Montana Earthquake Reading

We know the Montana earthquake was 3.16 times as powerful as the Idaho earthquake, which measured 7.2. The equation for comparing their powers is: \[ M = 7.2 + rac{log(3.16)}{log(10)} \] Calculating this gives us: \[ M \approx 7.2 + 0.5 = 7.7 \] Therefore, the Richter scale reading for the Montana earthquake was 7.7.
03

Compare Idaho and Arizona Earthquakes

To compare the power of the Idaho and Arizona earthquakes, we use the relationship of magnitude difference on the Richter scale:\[ ext{Power ratio} = 10^{(7.2 - 5.6)} \] Thus, \[ ext{Power ratio} \approx 10^{1.6} \approx 39.8 \] Therefore, the Idaho quake was about 39.8 times more powerful than the Arizona quake.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Earthquake Magnitude
Earthquake magnitude is a crucial concept in understanding the power of an earthquake. This measurement reflects the energy released at the source of the earthquake. The magnitude determines how much energy waves emit from the earthquake's focus, impacting the surrounding regions.
Unlike the intensity, which evaluates the earthquake's effects and damage, magnitude is a quantifiable figure independent of the location and depth.
In the original exercise, the magnitude is used to compare different earthquakes. For instance, the Montana earthquake had a magnitude of 7.7, which was calculated based on its power relative to the Idaho earthquake with a magnitude of 7.2. Understanding the concept of magnitude helps scientists estimate the potential energy release, aiding in preparedness and risk assessment.
Logarithmic Scale
A logarithmic scale is a crucial component of the Richter scale. This concept means that each point increase on the scale signifies an exponential change in measurement.
In terms of earthquakes, a one-point increase in magnitude on the Richter scale means the seismic waves' amplitude is ten times greater and releases approximately 31.6 times more energy.
  • For example, a 7.0-magnitude quake is about 10 times the amplitude of a 6.0 magnitude quake.
  • Energy release differs more dramatically 鈥� a 7.0 magnitude is over 31 times stronger in energy release compared to a 6.0 magnitude.
This logarithmic nature provides a more manageable way to represent and compare the immense energy involved in earthquakes. In the exercise, this scale is used to interpret the power differences between the Idaho and the Arizona earthquakes through magnitude comparisons.
Seismology
Seismology is the scientific study of earthquakes and the propagation of elastic waves through the Earth. This field is integral for understanding not only how and why earthquakes occur but also predicting them and mitigating their effects.
Seismologists use tools like the Richter scale to measure, analyze, and interpret earthquake data. This helps in determining the potential impact of an earthquake, assisting emergency services and public awareness efforts. By measuring earthquake magnitudes and understanding logarithmic relationships, researchers can make informed decisions about building codes and disaster planning.
In educational exercises, like the one provided, seismology principles are applied to understand the magnitude of various earthquakes and their comparative power. This connection between academic theory and practical application is essential for future advancements in earthquake preparedness and understanding.

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Most popular questions from this chapter

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