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S and P waves.

  1. Nov 18, 2003 #1
    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. [?]
     
  2. jcsd
  3. Nov 18, 2003 #2

    Doc Al

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    Staff: Mentor

    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.
     
  4. Nov 18, 2003 #3
    Thanks I knew it had something to do with that formula, and I figured it out.

    change in time = d/v1 - d/v2. :)
     
  5. Nov 18, 2003 #4

    chroot

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    Staff Emeritus
    Science Advisor
    Gold Member

    As you know,

    [tex]
    \begin{equation*}
    \begin{split}
    distance &= velocity \times time\\
    s &= v t
    \end{split}
    \end{equation*}
    [/tex]

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

    [tex]
    s = v_s t_s = v_p t_p
    [/tex]

    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

    [tex]
    t_s = t_p + 18.2
    [/tex]

    Substitute this into the previous equation:

    [tex]
    v_s (t_p + 18.2) = v_p t_p
    [/tex]

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

    - Warren
     
  6. Nov 18, 2003 #5

    chroot

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    Staff Emeritus
    Science Advisor
    Gold Member

    Yup. :smile:

    - Warren
     
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