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Math Help - Elastic modulus, earthquake waves?

  1. #1
    Member realintegerz's Avatar
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    Elastic modulus, earthquake waves?

    A longitudinal earthquake wave strikes a boundary between two types of rock at a 35 degree angle. As it crosses the boundary, the specific gravity (SG = d_rock / d_water ) of the rock changes from 3.7 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.

    To solve this I have two equations.

    1) (velocity 1/ velocity 2) = (sine angle 1 / sine angle 2), a ratio

    2) velocity of an earthquake wave = sq. root ( elastic modulus / density )

    The problem I'm having is, I don't know what the elastic modulus is and what the density or (rho) is, and also density is supposed to = m/v

    Otherwise, I could solve this easily...

    Can anyone help?
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  2. #2
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    Quote Originally Posted by realintegerz View Post
    A longitudinal earthquake wave strikes a boundary between two types of rock at a 35 degree angle. As it crosses the boundary, the specific gravity (SG = d_rock / d_water ) of the rock changes from 3.7 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.

    To solve this I have two equations.

    1) (velocity 1/ velocity 2) = (sine angle 1 / sine angle 2), a ratio

    2) velocity of an earthquake wave = sq. root ( elastic modulus / density )

    The problem I'm having is, I don't know what the elastic modulus is and what the density or (rho) is, and also density is supposed to = m/v

    Otherwise, I could solve this easily...

    Can anyone help?
    the problem says that the elastic modulus is the same for both types of rock, so it will cancel in the equation.


    \frac{v_1}{v_2} = \frac{\sqrt{\frac{e}{\rho_1}}}{\sqrt{\frac{e}{\rho  _2}}}

    \frac{v_1}{v_2} = \sqrt{\frac{\rho_2}{\rho_1}}

    you also know the respective SG's ...

    \frac{\rho_1}{\rho_w} = 3.7

    \frac{\rho_2}{\rho_w} = 2.8

    \frac{\frac{\rho_1}{\rho_w}}{\frac{\rho_2}{\rho_w}  } = \frac{3.7}{2.8}

    note that the value for water density also cancels ...

    \frac{\rho_1}{\rho_2} = \frac{3.7}{2.8}

    you should be able to finish up
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