Question

An increase of one on the Richter scale corresponds to an increase of 10 in the size of the largest wave on a seismogram. How many times larger is the largest wave of a Richter magnitude-6 earthquake than a Richter magnitude-3 earthquake?

Short answer

The largest wave of a Richter magnitude-6 earthquake is 1000 times larger than a Richter magnitude-3 earthquake.

Step-by-step solution

Understanding the Richter Scale

The Richter scale is logarithmic. This means that each whole number increase on the scale corresponds to a tenfold increase in the magnitude of the seismic waves.

Determine the Difference in Richter Scale

Calculate the difference in the magnitudes: \(6 - 3 = 3\). This means the magnitude-6 earthquake is 3 Richter scale points higher than the magnitude-3 earthquake.

Calculate the Magnitude Increase

Since each increase of 1 on the Richter scale corresponds to a 10 times increase in wave size, raising to the power of 3 (the difference in magnitudes) gives: \(10^3\).

Compute the Result

Calculate \(10^3\), which equals 1000. Thus, a magnitude-6 earthquake has waves that are 1000 times larger than those of a magnitude-3 earthquake.

Key concepts

Logarithmic Scale

The Richter scale is a perfect example of a logarithmic scale, which may at first seem complex, but let's make it simple. On this type of scale, each unit increase represents a tenfold change in the quantity being measured. This means that as you move up one number on a logarithmic scale, the quantity increases by a factor of 10. In the case of the Richter scale, this quantity is the amplitude of the seismic waves recorded during an earthquake.

Imagine you have a seismogram, a tool used to record the motion of the ground during an earthquake. When the needle jumps on this recording, it measures the wave amplitude. Due to the logarithmic nature of the Richter scale, an increase from 5 to 6 is not just a small bump but means the amplitude is ten times larger!

This is similar to how sound is measured in decibels; a small increase in the number can mean a big increase in sound strength. By using a logarithmic scale, scientists can handle the vast range of seismic activities in an intuitive way, making it easier to understand just how strong each earthquake truly is.

Seismogram

At the heart of earthquake measurement is the seismogram. A seismogram is the detailed record a seismometer produces when it detects and measures ground motion. Imagine it like a heartbeat monitor, but for the Earth. During an earthquake, it tracks the size and timing of waves crossing the Earth.

• The squiggles you see on a seismogram represent the Earth's movements.
• Each peak correlates to the arrival time of different earthquake waves, such as P-waves and S-waves.
• The height of these peaks tells us how powerful the waves are.

So, when an earthquake occurs, the largest wave captured on the seismogram is pivotal in determining the earthquake's magnitude. The greater the amplitude, the higher the recorded magnitude on the Richter scale. Therefore, if the Richter scale indicates a 6 instead of a 3, it directly relates to much larger seismic waves being imprinted on the seismogram. Understanding and interpreting these records allow scientists to quantify the energy released during earthquakes effectively.

Magnitude of Earthquakes

The magnitude of earthquakes is a crucial number that conveys the earthquake's size or energy release. Derived from the Greek word 'megas' meaning 'great,' the magnitude reveals the total seismic energy radiated by an earthquake.

The measurement starts when the seismogram captures the seismic waves. Then, with the help of mathematical formulas and adjustments based on distance and media through which the waves travel, the earthquake's magnitude is determined and expressed on the Richter scale.

It's essential to remember that:

• The magnitude is dimensionless - a simple, clean number.
• Each whole number step represents a significant increase in energy release.
• A magnitude 6 earthquake has far more destructive potential than a magnitude 3 because the energy difference isn’t 3-fold, but 1000-fold.

This logarithmic progression helps not only in quantifying the immediate impact but also in preparing for potential aftereffects and necessary responses to ensure safety.