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Wavelength - how far away did earthquake occur

  1. Dec 4, 2007 #1
    1. The problem statement, all variables and given/known data

    Assuming typical speeds of 8.9 km/s and 5.8 km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 1.0 min apart?
    _____km


    2. Relevant equations

    v=(lamba)(f)
    1/T=frequncy
    lamba=one wave length
    T=period

    X=same

    Vpwave=deltaX/T

    Vswave=dletaX/T+60

    3. The attempt at a solution

    8.9=

    5.8=
     
  2. jcsd
  3. Dec 4, 2007 #2

    dynamicsolo

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    Homework Helper

    This is basically what you need. Solve the first equation for an expression for T and substitute it into the second equation, so you can eliminate the unknown T. You now have an equation you can solve for deltaX.

    [As a check, consider this. Both types of waves started from the same "source". About how much do the P-waves gain on the S-waves each second? How much longer do the S-waves need to make up the difference? How long will it take for the S-waves to be a full minute behind? How far will the P-waves have traveled in that time? The algebraic solution described above is equivalent to answering these questions.]
     
    Last edited: Dec 4, 2007
  4. Dec 5, 2007 #3
    Vp=deltaX/T
    VpT=deltaX
    T=deltaX/Vp

    Vs=deltaX/T+60
    Vs(T+60)=deltaX
    VsT+Vs60=deltaX
    T=deltaX-Vs60/Vp

    deltaX-Vs60/Vp=deltaX/Vp
    deltaX-Vs60=deltaX
    deltaX=Vs60

    Is this how you solve for deltaX
     
  5. Dec 5, 2007 #4

    dynamicsolo

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    You were OK to here. The next line would then be

    T = (deltaX - Vs·60)/Vs ,

    so from there,

    (deltaX - Vs·60)/Vs=deltaX/Vp

    (deltaX/Vs) - (deltaX/Vp) = 60

    (deltaX) · [ (1/Vs) - (1/Vp) ] = 60

    delta X = [ (Vs·Vp) / (Vp - Vs) ] · 60
     
  6. Dec 5, 2007 #5
    i got the answer but just wondering how you got from:

    (deltaX - Vs·60)/Vs=deltaX/Vp

    to

    (deltaX/Vs) - (deltaX/Vp) = 60
     
  7. Dec 5, 2007 #6

    dynamicsolo

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    (deltaX - Vs·60)/Vs = deltaX/Vp

    (deltaX)/Vs - (Vs·60)/Vs = deltaX/Vp

    (deltaX)/Vs - (60) = deltaX/Vp

    (deltaX/Vs) - (deltaX/Vp) = 60

    In fact, you could really start right from here because this just says that the difference between the time it takes the S-waves to reach the station and the time it takes for the P-waves to do so is 60 seconds.
     
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