Question

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

Answer 1

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.