Earthquake analysis (motion along a straight line)

[physstudent1]

Homework Statement

Earthquakes produce several types of shock waves. The most well known are the P-waves (primary or pressure) and the S-waves (secondary or shear). In the Earth's crust, the P-waves travel at around 6.5km/s, while the S-waves move at about 3.5km/s. The actual speeds vary depending on the type of material they are going through. The time delay between the arrival of these two waves at a seismic recording station tells geologists how far away the earthquake occurred. If the time delay is 33s, how far from the seismic station did the earthquake occur?

Homework Equations

The Attempt at a Solution

I figured that the time delay will mean after the first P-wave is recorded it takes 33 seconds for the S-wave to get there, meaning the P-wave will get there in some time and then the S-wave will get there in some time + 33 seconds.

So I set up:
3.5(33+t) = 6.5t
t=38.5 seconds which is how long the P-wave traveled;
Which means the displacement from where the earthquake started is 38.5(6.5) = 250km. I'm not sure if this is right or the right way to do it if someone could just check over it that would be great, thanks.

 

[Archduke]

Hey, I just went through your calculations, and it looks good to me. A quick way to check if you had the right answer is like this:

$$\Delta t = t_{s} - t_{p} = \frac{250.25 km}{3.5 km s^{-1}} - \frac{250.25 km}{6.5 kms^{-1}} = 33s$$

Which obviously shows you're right. Well done!

 

[m2003]

Your solution to the problem is correct. By using the equation d = vt, where d is the distance, v is the velocity, and t is the time, you were able to calculate the distance from the seismic station to the location of the earthquake. This is a common method used by scientists to determine the epicenter of an earthquake. However, it is important to note that the actual speeds of the P-waves and S-waves may vary depending on the type of material they are traveling through. This can affect the accuracy of the distance calculation, but it is still a useful method for determining the general location of the earthquake. Additionally, there are other factors that can affect the arrival times of these waves at a seismic station, such as the depth of the earthquake and the location of the station in relation to the epicenter. Overall, your solution is a valid approach to solving this problem and demonstrates an understanding of earthquake analysis and the use of scientific equations.