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Chapter 9: Problem 133

Earthquakes. In \(1985,\) Mexico City experienced an earthquake of magnitude 8.1 on the Richter scale. In \(1989,\) the San Francisco Bay area was rocked by an earthquake measuring \(7.1 .\) By what factor must the amplitude of an earthquake change to increase its severity by 1 point on the Richter scale? (Assume that the period remains constant.)

Short Answer

Expert verified
The amplitude must change by a factor of 10 to increase the Richter scale by 1 point.

Step by step solution

01

Understanding the Richter Scale

The Richter scale is logarithmic, meaning that each whole number step on the Richter scale corresponds to a tenfold increase in amplitude. Thus, an earthquake that increases by 1 magnitude on the Richter scale is 10 times stronger in terms of shaking amplitude.
02

Comparing Earthquake Magnitudes

Given the problem, we're asked to find by what factor the amplitude changes when the magnitude changes by 1 point on the Richter scale. Since the scale is logarithmic, increasing by 1 point means the amplitude must increase by a factor of 10.
03

Implication of a 1-Point Increase

A 1-point increase on the Richter scale implies a multiple of the original amplitude. Specifically, this means that if we increase the magnitude by 1, the amplitude becomes 10 times that of the original earthquake.
04

Conclusion

Therefore, to increase the earthquake's magnitude by 1 point on the Richter scale, the amplitude of the earthquake must change by a factor of 10.

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Key Concepts

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

Logarithmic Scale
A logarithmic scale is a type of scale used to depict data that spans a broad range of values. Instead of each step increasing linearly, as in a standard scale, every step on a logarithmic scale represents an exponential increase.
In the case of the Richter scale, which is a logarithmic scale, each whole number increment represents a tenfold increase in seismic wave amplitude. This scale is especially useful for measuring phenomena like earthquakes, where the differences in values can be vast.
  • Every increase of 1 on the Richter scale translates to an earthquake releasing 31.6 times more energy.
  • This scale allows us to handle the wide variation in earthquake sizes in a manageable way, making it easier to compare small and massive quakes.
Logarithmic scales are common in sciences because they efficiently represent differences without requiring enormous numeric spaces.
Earthquake Magnitude
Magnitude is a measure of the size or energy release of an earthquake. Specifically on the Richter scale, magnitude denotes the logarithm of the maximum amplitude of seismic waves observed on a standard seismometer.
A slight increase in magnitude can indicate a huge jump in actual size due to the logarithmic nature of the measure. Some key points about earthquake magnitude include:
  • Magnitude assesses the energy released, rather than describing all the different possible effects of the earthquake.
  • Magnitude does not change with location; it will be the same no matter where you measure it.
This means an earthquake measured at a magnitude of 8 is not two times as strong as a magnitude 4 earthquake. Instead, it's many times more powerful, as each point increase equates to significant energy amplifications.
Amplitude
In the context of earthquakes, amplitude refers to the size or height of the seismic waves as they are recorded on a seismograph. The larger the amplitude, the more intense the shaking of the earthquake.
Amplitude is critically important to understanding the destructive potential of an earthquake. Some important details about amplitude include:
  • It reflects the physical shaking observed during the event.
  • On the Richter scale, a 1-point increase results in a tenfold increase in wave amplitude.
This exponential increase is why areas with higher Richter scale readings tend to see more damage. The sheer size of the waves captured in the higher readings means more shaking and therefore more potential for destruction.

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