Problem 10 - Prealgebra

Question

In \(2005,\) an earthquake measuring 5 on the Richter scale struck the Philippines. Four days later, an earthquake of magnitude 3 struck Southern Alaska. How many times greater were the seismic waves in the Philippines than in Alaska?

Step-by-Step Solution

Answer

The seismic waves in the Philippines were 100 times greater in amplitude than in Alaska.

Step 1: Understanding the Richter Scale

The Richter scale is logarithmic, meaning each whole number increase on the scale represents a tenfold increase in measured amplitude and roughly 31.6 times more energy release. This means an earthquake with a magnitude of 5 has much more powerful seismic waves than one with a magnitude of 3.

Step 2: Calculating the Wave Amplitude Ratio

To find how many times greater the seismic waves were, calculate the ratio of the wave amplitudes using the formula: \(10^{M_1 - M_2}\). Here, \(M_1 = 5\) (Philippines) and \(M_2 = 3\) (Alaska). So, the calculation is \(10^{5-3} = 10^2 = 100\).

Step 3: Interpreting the Result

The result of the calculation, \(100\), means that the seismic waves in the Philippines were 100 times greater in amplitude than those in Alaska during these events.

Key Concepts

Understanding Earthquake Magnitude

When we talk about an earthquake's magnitude, we refer to the size or strength of the seismic event. This is often measured using the Richter Scale, which helps scientists quantify just how powerful an earthquake is. The magnitude of an earthquake tells us about the *energy released* from the earthquake's source. It's an objective measure that remains consistent regardless of where it's measured, allowing for accurate comparisons between different seismic events.

• A higher magnitude means a more intense earthquake.
• Every increase of 1 in magnitude signifies a dramatic increase in strength.

This scale does not measure the damage an earthquake may cause, which can depend on other factors such as depth and location.

Exploring the Logarithmic Scale

The Richter Scale is a perfect example of a logarithmic scale. This type of scale is used because seismic waves can vary enormously in amplitude and energy. On a logarithmic scale:- Each increase by 1 in magnitude represents a tenfold increase in the amplitude of the seismic waves.- Also, the energy release increases about 31.6 times for each whole number increase.For instance, if one earthquake measures 5 and another measures 3 on the Richter Scale, the amplitude of the waves differs by a factor of 100. This is calculated using the formula:\[ 10^{M_1 - M_2} = 10^{5 - 3} = 10^2 = 100 \]Such a scale makes it easier to represent and compare events that vary widely in strength, enabling us to understand massive differences in their potential impact.

Understanding Seismic Waves

Seismic waves are the energy that radiates out from an earthquake's focal point. These waves can be felt over large distances and studied to gain insights into the earthquake's characteristics. Seismic waves can be broken down into several types:

• **Primary waves (P-waves)**: These are the fastest and first to be detected by seismographs. They compress and expand the ground like sound waves do in air.
• **Secondary waves (S-waves)**: These are slower than P-waves and can only move through solid material, not through liquid.
• **Surface waves**: Traveling over the Earth's surface, they cause the most damage due to their high amplitude and energy.

Understanding these different types allows scientists to determine the earthquake's magnitude, location, and deeper insights into Earth's interior. During seismic events of different magnitudes, these wave properties change dramatically, explaining why higher magnitude earthquakes can be so much more destructive.