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 7707.0m/s. Transverse waves, called S waves, travel at a slower 3800.0m/s. A seismograph records the two waves from a distant earthquake. If the S wave arrives 3.82min 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 7707.0m/s. Transverse waves, called S waves, travel at a slower 3800.0m/s. A seismograph records the two waves from a distant earthquake. If the S wave arrives 3.82min 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

since the distances are the same, and

distance = speed * time
then, using t as seconds,

7707t = 3800(t+229.2)
t = 222.92 s

7707*222.92 = 1718044m = 1718 km

Answer 2

To determine the distance of the earthquake, we can use the fact that the time difference between the arrival of the P wave and the S wave is related to the distance traveled by the seismic waves.

Let's start by converting the time difference from minutes to seconds:
3.82 minutes x 60 seconds/minute = 229.2 seconds

Now, we can use the formula for distance traveled by a wave:
Distance = Speed x Time

For the P wave:
Distance_P = Speed_P x Time_P

And for the S wave:
Distance_S = Speed_S x Time_S

Since we are given the speed of the P wave (7707.0 m/s) and the speed of the S wave (3800.0 m/s), we can substitute these values into the formulas:

Distance_P = 7707.0 m/s x Time_P
Distance_S = 3800.0 m/s x (Time_P + 229.2 seconds)

Since the distance traveled by both waves is the same (the earthquake source), we can equate the two distances:

7707.0 m/s x Time_P = 3800.0 m/s x (Time_P + 229.2 seconds)

Now, let's solve for Time_P:

7707.0 m/s x Time_P = 3800.0 m/s x Time_P + 3800.0 m/s x 229.2 seconds

Simplifying the equation:

7707.0 m/s x Time_P - 3800.0 m/s x Time_P = 3800.0 m/s x 229.2 seconds

3907.0 m/s x Time_P = 3800.0 m/s x 229.2 seconds

Now, let's solve for Time_P:

Time_P = (3800.0 m/s x 229.2 seconds) / (7707.0 m/s - 3800.0 m/s)

Time_P = (869760 seconds) / (3907.0 m/s)

Time_P ≈ 222.648 seconds

Now, we have the value for Time_P, which represents the time it takes for the P wave to arrive. To find the distance, we can substitute this value back into the distance formula for the P wave:

Distance_P = 7707.0 m/s x Time_P

Distance_P = 7707.0 m/s x 222.648 seconds ≈ 1,713,350.536 meters

Therefore, the earthquake was approximately 1,713,350.536 meters away.