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 7558.0 m/s. Transverse waves, called S waves, travel at a slower 4175.0 m/s. A seismograph records the two waves from a distant earthquake. If the S wave arrives 4.14 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.
D/4175 - D/7558 = 4.14 min = 248 s
Solve for D, which wil be in meters
To find the distance to the earthquake, we can use the formula:
Distance = Speed * Time
Let's start by converting the time from minutes to seconds (since the speeds are given in meters per second). We know that 1 minute is equal to 60 seconds, so:
Time = 4.14 min * 60 s/min = 248.4 seconds
Now, we can use the formula to find the distance traveled by the P wave and the S wave:
Distance_P = Speed_P * Time = 7558.0 m/s * 248.4 s = 1,876,729.2 meters
Distance_S = Speed_S * Time = 4175.0 m/s * 248.4 s = 1,036,380 meters
Since seismic waves travel in straight lines, the total distance traveled by the waves is the sum of the distances traveled by the P wave and the S wave:
Total Distance = Distance_P + Distance_S
= 1,876,729.2 meters + 1,036,380 meters
= 2,913,109.2 meters
Therefore, the earthquake was approximately 2,913,109.2 meters away.