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tester [92]
3 years ago
9

Earth’s Science unit 2 lesson 15 laboratory: Earthquakes Epicenter

Chemistry
1 answer:
Olegator [25]3 years ago
3 0

Distance between the Tulsa, OK observatory and the center of this fictional earthquake: 20 kilometers.

An earthquake generates two major seismic waves that travel through the crest at different speeds:

  • Primary (P) waves travel at between 6 and 7 \text{km} \cdot \text{s}^{-1}
  • Secondary (S) waves travel at approximately 3.5 \text{km} \cdot \text{s}^{-1}.

Let v_\text{P} and v_{\text{S}} denote the speed of the two waves, respectively. Let t_\text{P}, t_\text{S} resembles the time required for each waves to reach the observatory.

Both t_\text{P} \cdot v_\text{P} and t_\text{S} \cdot v_\text{S} would represent the separation between the source and the observatory. Thus

t_\text{P} \cdot v_\text{P} = d\\t_\text{S} \cdot v_\text{S} = d\\

t_\text{P} = d / v_\text{P}\\t_\text{S} = d / v_\text{P}

Given the difference between  t_\text{P} and t_\text{S}:

t_\text{S} - t_\text{P} = 2.5 \; \text{minutes} = 150 \; \text{seconds}

(t_\text{P} < t_\text{S} given that v_\text{P} > v_\text{S} and  1/ v_\text{P} < 1/ v_\text{S})

d / v_\text{S} - d / v_\text{P} = t_\text{S} - t_\text{P} = 150 \; \text{seconds}\\d \cdot (1/v_\text{S} - 1/v_\text{P}) = 150 \; \text{seconds}

d = 150 \; \text{s} / ((1/(3.5 \; \text{km} \cdot \text{s}^{-1}) - 1/(6.5 \; \text{km} \cdot \text{s}^{-1}))\\\phantom{d} =2.0 \times 10\; \text{km} = 20 \; \text{km}

Note that wave speed data involved in calculations above came from an external source. You shall repeat those steps with speeds indicated on the worksheet if possible.

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