How Far Away Was the Earthquake if S Waves Arrived 2 Minutes After P Waves?

[Foxhound101]

Homework Statement

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 8000 m/s . Transverse waves, called S waves, travel at a slower 4500 m/s . A seismograph records the two waves from a distant earthquake.

Part A
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.
Express your answer using two significant figures.

time=120 seconds
v=8000 m/s
v=4500 m/s

Homework Equations

V=D/t

The Attempt at a Solution

Not sure how to solve the problem. I tried to calculate how far each wave traveled in 120 seconds, but I don't know what to do after that. There might be other formulas I am supposed to use, but I don't know which ones.

8000m/s = D/120sec
D=960000m

and

4500m/s = D/120sec
D=540000

 

[alphysicist]

Hi Foxhound101,

Homework Statement

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 8000 m/s . Transverse waves, called S waves, travel at a slower 4500 m/s . A seismograph records the two waves from a distant earthquake.

Part A
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.
Express your answer using two significant figures.

time=120 seconds
v=8000 m/s
v=4500 m/s

Homework Equations

V=D/t

The Attempt at a Solution

Not sure how to solve the problem. I tried to calculate how far each wave traveled in 120 seconds, but I don't know what to do after that. There might be other formulas I am supposed to use, but I don't know which ones.

8000m/s = D/120sec
D=960000m

and

4500m/s = D/120sec
D=540000

The time of travel for each wave is not equal to 120 seconds; the times are unknown (though you can solve for them) so you can put the variables t₁ and t₂ into your equations. Then the important thing is how these different times are related to each other, so that you can eliminate either t₁ or t₂ and solve for D. What do you get?

 

[Foxhound101]

Hi alphysicist, thanks for responding.

Hi Foxhound101,



The time of travel for each wave is not equal to 120 seconds; the times are unknown (though you can solve for them) so you can put the variables t₁ and t₂ into your equations. Then the important thing is how these different times are related to each other, so that you can eliminate either t₁ or t₂ and solve for D. What do you get?

And that is the kind of thing I am terrible at...

So...Something like this?

8000m/s = D/T₁
4500m/s = D/(T₁+120)

T₁=D/8000

4500 = D/(D/8000 + 120)

 

[alphysicist]

Hi alphysicist, thanks for responding.



And that is the kind of thing I am terrible at...

So...Something like this?

8000m/s = D/T₁
4500m/s = D/(T₁+120)

T₁=D/8000

4500 = D/(D/8000 + 120)

I believe that will give you the correct answer. What do you get for D?

 

[Foxhound101]

I got 274.29 which for the MasteringPhysics program I changed into 270. The program still says that is the wrong answer, however.

4500 = 8000D/(D+120(8000))

4500(D+120(8000))=8000D

120(8000)=8000D-4500D

D=274.29

 

[alphysicist]

I got 274.29 which for the MasteringPhysics program I changed into 270. The program still says that is the wrong answer, however.

4500 = 8000D/(D+120(8000))

4500(D+120(8000))=8000D

120(8000)=8000D-4500D

This line does not follow from the previous one. The 4500 is multiplying the D and is also multiplying the 120(8000).

D=274.29

If you consider that answer you can see why it does not make sense. Since the waves go multiple thousands of meters every second, both wave would go a distance of 275 m in less than a second, so there is no way that one wave would be two minutes behind the other.

 

[Foxhound101]

Does 1.2*10^6 make any more sense?

 

[alphysicist]

Does 1.2*10^6 make any more sense?

Well, you might want to keep more digits, but you can check it to see if it works. Find the two times from your original equations:

<br /> \begin{align}<br /> 8000&amp;=(1.2\times 10^6)/t_1\nonumber\\<br /> 4500&amp;=(1.2\times 10^6)/t_2\nonumber<br /> \end{align}<br />
and then once you have t₁ and t₂, you can check to see if they are 120 seconds apart. (But like I said, to get it right at 120 seconds apart, you might need to keep at least three digits in your answer for D.)

 

[Foxhound101]

Thanks for your help alphysicist. The program only wants 2 significant digits and that is why I used 1.2*10^6 instead of a more accurate number.

And that was the correct answer. You have been very helpful.

One last thing.

Once your problem has been solved or your questions have been answered, take a moment to mark the problem thread as SOLVED. That makes it easier for homework helpers to know who still needs help.

I would like the mark this problem/thread as solved, but I don't see it under thread tools.

 

[alphysicist]

Thanks for your help alphysicist. The program only wants 2 significant digits and that is why I used 1.2*10^6 instead of a more accurate number.

And that was the correct answer. You have been very helpful.

One last thing.

Once your problem has been solved or your questions have been answered, take a moment to mark the problem thread as SOLVED. That makes it easier for homework helpers to know who still needs help.

I would like the mark this problem/thread as solved, but I don't see it under thread tools.

After a website update, users lost the ability to mark threads as solved. As far as I know that has not changed yet, but I think they are planning on bringing it back. (Perhaps someone who knows more than me about it will post more information here.)