What equation do I use?

  • Thread starter jjlandis
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In summary, in this conversation the topic of earthquake shock waves and their velocities is discussed. The P-waves and S-waves travel at different speeds, with P-waves traveling at 7.0 km/s and S-waves traveling at 3.6 km/s. The time delay between their arrival can be used to determine the distance of the earthquake from the seismic station. The given time delay of 19 seconds results in a distance of 140.8 meters. The solution method is also mentioned, using the equations Vs*ts = xs and Vp*tp = xp to calculate the distance from the seismic station.
  • #1
jjlandis
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Homework Statement


Earthquakes produce several types of shock waves. The most well-known are the P-waves and the S-waves. In the earth’s crust, the P-waves travel around 7.0 km/s while the S-waves move at about 3.6 km/s. 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 19 s, how far away from the seismic station did the earthquake occur?
Answer in book is 140.8 m but I can't make it to that answer. Any help would be great.
Thanks.


Homework Equations






The Attempt at a Solution


Tried to find the x distance by using: X-Xo = ((Vox + Vx)*.5)*t
 
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  • #2
jjlandis said:

Homework Statement


Earthquakes produce several types of shock waves. The most well-known are the P-waves and the S-waves. In the earth’s crust, the P-waves travel around 7.0 km/s while the S-waves move at about 3.6 km/s. 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 19 s, how far away from the seismic station did the earthquake occur?
Answer in book is 140.8 m but I can't make it to that answer. Any help would be great.
Thanks.

Homework Equations



The Attempt at a Solution


Tried to find the x distance by using: X-Xo = ((Vox + Vx)*.5)*t

The average velocity isn't going to identify the distance now is it since you don't know the actual time really. They arrive at different times.

But they do arrive from the same distance X.

Vs*ts = xs

Vp*tp = xp

where xs = xp = X

Consider then Δt between the slow one and the fast one. That gives you distance then doesn't it? And they do give you conveniently Δt.
 
  • #3

Where Xo = 0 and Vx = 3.6 km/s and Vox = 7.0 km/s
But I am getting an answer of 38.8 km, which is not close to the given answer of 140.8 m.
Can someone please explain the correct equation to use for this problem?

Dear student,

The equation you are using is the correct one, but you have made a small mistake in your calculations. The correct equation to use for this problem is:

x = (Vp + Vs)*t/2

Where:
- x is the distance from the seismic station to the earthquake's epicenter
- Vp is the velocity of P-waves (7.0 km/s)
- Vs is the velocity of S-waves (3.6 km/s)
- t is the time delay between the arrival of P-waves and S-waves (19 s)

Plugging in the values, we get:
x = (7.0 km/s + 3.6 km/s)*19 s/2 = 10.6 km * 9.5 s = 100.7 km

This is the distance in kilometers, but the answer given in the book is in meters, so we need to convert it:
100.7 km = 100,700 m

Therefore, the correct answer is 100,700 m or 100.7 km.

I hope this helps clarify the equation and solve the problem. Remember to always double check your calculations to avoid any mistakes. Keep up the good work!
 

1. What is the difference between an equation and a formula?

An equation is a mathematical statement that shows the relationship between two or more variables, while a formula is a specific type of equation that provides a step-by-step process for solving a problem or finding a value. In other words, a formula is a type of equation, but not all equations are formulas.

2. How do I determine which equation to use for a specific problem?

The equation you use will depend on the specific problem you are trying to solve. It is important to first understand the problem and identify the known and unknown variables. Then, you can look for an equation that relates those variables and use it to solve the problem.

3. What is the difference between linear and nonlinear equations?

A linear equation is one in which the variables are only raised to the first power and the graph of the equation is a straight line. Nonlinear equations, on the other hand, can have variables raised to any power and their graphs are not straight lines. Nonlinear equations can have multiple solutions, while linear equations only have one solution.

4. Can the same equation be used for different problems?

Yes, the same equation can be used for different problems as long as the variables involved are the same and the relationship between them is consistent. However, it is important to check that the equation is applicable to the specific problem you are trying to solve.

5. How can I check if my equation is correct?

You can check if your equation is correct by plugging in known values for the variables and solving for the unknown variable. Then, check if the answer matches the expected result. Additionally, you can use mathematical principles such as the order of operations and unit conversions to verify the accuracy of your equation.

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