Question

Use an atlas and a metric rule to answer the following question. Primary waves travel at about \(6 \mathrm{~km} / \mathrm{s}\) in continental crust. How long would it take a primary wave to travel from San Francisco, California, to Reno, Nevada?

Short answer

It takes approximately 58.33 seconds.

Step-by-step solution

Determine the Distance

First, we need to find the distance between San Francisco, California, and Reno, Nevada. Using an atlas, locate both cities and use the map scale to measure the distance directly. Let's say the distance measured is approximately 350 kilometers.

Use the Wave Speed Formula

Given the speed of primary waves as 6 km/s, we need to use the formula for speed, which is \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\). Rearranging to find time gives: \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\).

Calculate the Time

Substitute the known values into the formula: \[\text{Time} = \frac{350 \text{ km}}{6 \text{ km/s}} = \frac{350}{6} \text{ s} \approx 58.33 \text{ seconds}\].

Key concepts

Primary Waves

Primary waves, often termed P-waves, are a type of seismic wave that play an essential role in the study of earthquakes and Earth's internal structure. They are the fastest seismic waves and the first to be detected by seismographs. These waves are capable of moving through solids, liquids, and gases, which is unique compared to other seismic waves.

The movement of P-waves is often compared to the motion of a slinky. They compress and expand the material they move through in the direction they are traveling. This compressional movement is why they are also referred to as pressure waves.

In the context of continental crust, P-waves generally travel at a speed of about 6 km/s. This rapid speed allows them to cover large distances in short periods, making them critical in determining the characteristics of seismic events, as well as the structure and composition of Earth's interior.

Wave Speed Formula

The wave speed formula is a fundamental equation used in physics to relate the speed of a wave to the distance it travels and the time it takes. This formula is particularly useful across different types of waves, including seismic waves such as primary waves.

The formula states:

• Speed = \( \frac{\text{Distance}}{\text{Time}} \)
• To find the speed of the wave from a known distance and time, simply rearrange the formula to solve for speed.
• Time = \( \frac{\text{Distance}}{\text{Speed}} \)

If you need to find out how long it takes a wave to travel a certain distance (as in our exercise), reposition the formula to solve for time. This rearrangement is practical because it enables us to interpret various scenarios where any two of the variables are known.

Understanding this equation helps in analyzing real-world situations involving waves, such as determining how quickly seismic information can be relayed following an earthquake.

Distance Measurement

Distance measurement is a critical component when applying the wave speed formula, particularly in seismic studies. An atlas or map is commonly used to measure the distances between geographic locations, such as from San Francisco to Reno in our example.

When using a map to determine distance, ensure that you are using the correct scale given by the map. This usually involves measuring the distance on the map with a ruler and then converting it using the scale provided. This helps in approximating real-world distances.

Let's say you measure the distance on a map and find it to be 350 kilometers, as we have seen in the San Francisco to Reno example. Accurately determining this distance is crucial, as any error will subsequently affect the calculations using the wave speed formula. Proper measurement and conversion ensure that time calculations (like the travel time of primary waves) are as accurate as possible.