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 8982.0 m/s. Transverse waves, called S waves, travel at a slower 4355.0 m/s. A seismograph records the two waves from a distant earthquake. If the S wave arrives 2.10 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 8982.0 m/s. Transverse waves, called S waves, travel at a slower 4355.0 m/s. A seismograph records the two waves from a distant earthquake. If the S wave arrives 2.10 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

Distance = (wave speed) x (time)

Let T1 be the time it takes the slower S wave to arrive, and T2 be the time is takes the P wave to arrive.

D = 4355 T1
D = 8982 T2

All you know is T1 - T2

T1 - T2 = D(1/4355 - 1/8982) = 126 s

Solve for D

Solve for D. Make sure T is in seconds. D will be im meters

Answer 2

the answer i got was correct, but how did you get the formula:

T1 - T2 = D(1/4355 - 1/8982) = 126 s ?

Answer 3

never mind...i figured it out

but when given the question, how did you know that you had to subtract the velocities?

Answer 4

I did not subtract the velocities. I subtracted the reciprocals of the velocities.

All you know initially is the difference between the wave travel times. You do not know the wave travels times themeselves. (But you can solve for them later).
The equation I used relates the difference in arrival times to the two wave velocities and the distance.

Answer 5

To determine the distance of the earthquake, we can use the information provided: the speed of the P waves (P_speed = 8982.0 m/s), the speed of the S waves (S_speed = 4355.0 m/s), and the time delay between the arrival of the S wave and P wave (time_delay = 2.10 min).

First, we need to convert the time delay from minutes to seconds. Since 1 minute is equal to 60 seconds, the time_delay in seconds would be:

time_delay_seconds = 2.10 min × 60 s/min = 126 seconds

Now, let's use the formula for calculating distance:

distance = speed × time

Since the waves travel in straight lines, we can assume that the distance travelled by the P wave is the same as the distance travelled by the S wave. Let's denote the distance as "d".

So, for the P wave, the distance travelled is:

distance_P = P_speed × time_delay_seconds

And for the S wave, the distance travelled is:

distance_S = S_speed × time_delay_seconds

Since both distances are equal, we have:

distance_P = distance_S = d

Substituting the given values:

8982.0 m/s × 126 s = 4355.0 m/s × 126 s = d

Simplifying the equation:

8982.0 m/s × 126 s = 4355.0 m/s × 126 s
1131192.0 m = 548730.0 m

Therefore, the distance of the earthquake is 1131192.0 meters or approximately 1131.2 kilometers.