Earthquakes are essentially sound waves traveling through the earth. They are called seismic waves. Because the earth is solid, it can support both longitudinal and transverse seismic waves. These travel at different speeds. The speed of longitudinal waves, called P waves, is 8000m/s. Transverse waves, called S waves, travel at a slower at 4500m/s . A seismograph records the two waves from a distant earthquake.
If the S wave arrives 2.0 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.
To determine the distance to the earthquake, we can use the formula:
Distance = Speed × Time
We'll assume that the P wave traveled for t minutes before the S wave arrived, so the total travel time for the P wave is t minutes, and the total travel time for the S wave is (t + 2) minutes.
The speed of the P wave is 8000 m/s, and the speed of the S wave is 4500 m/s.
Using the formula, we can set up two equations based on the speeds and travel times:
For the P wave:
Distance = 8000 (m/s) × (t min)
For the S wave:
Distance = 4500 (m/s) × (t + 2 min)
Since both distances are equal (the waves are traveling from the same earthquake source), we can set the two equations equal to each other:
8000 (m/s) × (t min) = 4500 (m/s) × (t + 2 min)
Now we can solve this equation to find the value of t:
8000t = 4500(t + 2)
8000t = 4500t + 9000
3500t = 9000
t ≈ 2.57 minutes
So, the P wave traveled for approximately 2.57 minutes before the S wave arrived.
To find the distance, we can substitute the value of t back into one of the original equations (let's use the equation for the P wave):
Distance = 8000 (m/s) × (2.57 min)
Distance ≈ 20560 meters
Therefore, the earthquake is estimated to be approximately 20560 meters away.