Solving a Seismic Mystery: Calculating Epicenter Distance

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The discussion revolves around calculating the distance from a seismographic station to an earthquake's epicenter using the time difference between S and P waves. The problem states that S and P waves arrive 18.2 seconds apart, traveling at speeds of 4.50 km/s and 7.00 km/s, respectively. The key to solving the problem lies in using the formula Distance = Speed x Time, along with the relationship between the travel times of the two waves. By substituting the time difference into the equations for both wave types, one can derive the time taken by the P wave and subsequently calculate the distance. The solution emphasizes the importance of understanding wave mechanics and algebraic manipulation in seismology.
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It seems to me that this is just a simple algebra problem, that doesn't have much to do with waves, but it's the only problem on the homework that I can't figure out. :-/ I know there's an easy solution to it, but I keep getting the wrong answer. Anyway, here it goes:

A seismographic station receives S and P waves from an earthquake, 18.2 s apart. Suppose that the waves have traveled over the same path, at speeds of 4.50 km/s and 7.00 km/s respectively. Find the distance from the seismometer to the epicenter of the quake.

Anyone have any help? I know the solution must be blindingly obvious. [?]
 
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Both S and P waves travel the same distance. Use the venerable formula, Distance = Speed x Time, to calculate D based on the difference in T.
 
Thanks I knew it had something to do with that formula, and I figured it out.

change in time = d/v1 - d/v2. :)
 
As you know,

<br /> \begin{equation*}<br /> \begin{split}<br /> distance &amp;= velocity \times time\\<br /> s &amp;= v t<br /> \end{split}<br /> \end{equation*}<br />

The distances are the same in each case, so you have

<br /> s = v_s t_s = v_p t_p<br />

where s,p denote the two kinds of waves.

The s wave takes 18.2 seconds to reach the detector than the p wave. This means

<br /> t_s = t_p + 18.2<br />

Substitute this into the previous equation:

<br /> v_s (t_p + 18.2) = v_p t_p<br />

Solve for t_p. You then know the time taken by the p-wave, and the speed of the p-wave, so the distance is easily found.

- Warren
 
Originally posted by tristan_fc
Thanks I knew it had something to do with that formula, and I figured it out.

change in time = d/v1 - d/v2. :)
Yup. :smile:

- Warren
 
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