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 . Transverse waves, called S waves, travel at a slower . A seismograph records the two waves from a distant earthquake.

Question

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 . Transverse waves, called S waves, travel at a slower . 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.

Answer 1

Vs and Vp were not given?

d = Vs t
d = Vp(t-120 seconds)
so
Vs t = Vp(t-120)
t (Vp-Vs)=120
t = 120/(Vp-Vs)
and
d = Vs t = 120 Vs / (Vp-Vs)

Answer 2

To determine the distance to the earthquake, we need to use the difference in arrival times of the P wave and the S wave. We are given that the S waves arrive 2.0 minutes after the P waves.

First, we need to determine the speed of the P waves and the S waves.

The speed of the P waves is faster than the speed of the S waves. Let's assume the speed of the P waves is v_p and the speed of the S waves is v_s.

Since the S wave arrives later, we can say that it traveled for 2.0 minutes longer than the P wave.

Using the formula: speed = distance / time, we can calculate the distance traveled by each wave.

Distance traveled by the P wave (d_p) = v_p * t, where t is the time taken by the P wave to reach the seismograph.

Distance traveled by the S wave (d_s) = v_s * (t + 2.0 minutes), where t is the time taken by the P wave to reach the seismograph.

Now, let's set up an equation using the distances:

d_s = d_p

v_s * (t + 2.0 minutes) = v_p * t

Now, we need to isolate the t variable:

v_s * t + 2.0 minutes * v_s = v_p * t

2.0 minutes * v_s = v_p * t - v_s * t

2.0 minutes * v_s = (v_p - v_s) * t

Finally, we can solve for t:

t = (2.0 minutes * v_s) / (v_p - v_s)

Now that we have the value for t, we can calculate the distance traveled by the P wave using one of the distance formulas:

d_p = v_p * t

Similarly, we can calculate the distance traveled by the S wave:

d_s = v_s * (t + 2.0 minutes)

Adding the distances traveled by the P and S waves will give us the total distance from the earthquake.

distance = d_p + d_s

It's important to note that the units for the speed of the waves and the time taken need to be consistent (e.g., meters per second, kilometers per hour, etc.).