Earthquakes are essentially sound waves travelling through the earth. They are called seismic waves. Because the earth is solid, it can support both longitudinal and transverse sismic waves, which travel at different speeds. The speed of longitudinal waves, called P waves, is 7274.0 m/s. Transverse waves, called S waves, travel at a slower 3803.0 m/s. A seismograph records the two waves from a distant earthquake. If the S wave arrives 4.47 min after the P wave, how far away was the earthquake? You can assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.

Question

Earthquakes are essentially sound waves travelling through the earth. They are called seismic waves. Because the earth is solid, it can support both longitudinal and transverse sismic waves, which travel at different speeds. The speed of longitudinal waves, called P waves, is 7274.0 m/s. Transverse waves, called S waves, travel at a slower 3803.0 m/s. A seismograph records the two waves from a distant earthquake. If the S wave arrives 4.47 min after the P wave, how far away was the earthquake? You can assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.

Answer 1

To find the distance to the earthquake, we can use the formula:

Distance = Speed × Time

We know that the speed of the P wave (longitudinal wave) is 7274.0 m/s, and the speed of the S wave (transverse wave) is 3803.0 m/s.

Let's convert the time delay of the S wave arrival from minutes to seconds. There are 60 seconds in a minute, so:

Time delay = 4.47 min × 60 s/min = 268.2 s

Now we can calculate the distance using the formula for each wave:

Distance P = Speed P × Time delay
Distance S = Speed S × Time delay

Plugging in the values:

Distance P = 7274.0 m/s × 268.2 s = 1952374.8 m
Distance S = 3803.0 m/s × 268.2 s = 1019834.6 m

Since the seismic waves travel in a straight line, the total distance to the earthquake is the sum of the distances traveled by each wave:

Total distance = Distance P + Distance S
Total distance = 1952374.8 m + 1019834.6 m = 2972209.4 m

Therefore, the earthquake was approximately 2,972,209.4 meters away.

Answer 2

To find the distance to the earthquake, we need to start by determining the time difference between the arrival of the P wave and the S wave. We are given that the S wave arrives 4.47 minutes after the P wave.

Since the wave speed is distance divided by time, we can set up the following equation for the P wave and S wave:

Distance = Speed × Time

Let's assume the distance D is the same for both waves. The time it takes for the P wave to reach the seismograph is T (in seconds), and the time it takes for the S wave to reach the seismograph is T + 4.47 minutes (or T + 267 seconds since 1 minute is equal to 60 seconds).

For the P wave: D = 7274.0 m/s × T
For the S wave: D = 3803.0 m/s × (T + 267)

By setting these two equations equal to each other, we can solve for T:

7274.0 T = 3803.0(T + 267)

Let's simplify the equation:

7274.0 T = 3803.0T + 3803.0 × 267

Now, let's solve for T:

7274.0T - 3803.0T = 3803.0 × 267

3471.0T = 3803.0 × 267

T = (3803.0 × 267) / 3471.0

T ≈ 292.54 seconds

Now that we have the time difference between the P wave and S wave (T ≈ 292.54 seconds), we can find the distance to the earthquake using the speed of the P wave (7274.0 m/s) and the formula: Distance = Speed × Time.

Distance = 7274.0 m/s × 292.54 s

Distance ≈ 2,127,016.96 meters

Therefore, the earthquake was approximately 2,127,016.96 meters away from the seismograph.