Respuesta :
Answer:
The earthquake in North Cascades was about 63 times greater than the earthquake that happened near Woodburn Oregon in 1993
Explanations:
Given the magnitude, M, of an earthquake in relation to the seismic waves, W, modeled by the equation below;
[tex]M=\log (\frac{w}{w_0})[/tex]If in 1872, the North Cascades suffered its largest known earthquake of magnitude 7.4, hence;
[tex]\begin{gathered} 7.4=\log (\frac{w}{w_o}) \\ (\frac{w}{w_o^{}})_n=10^{7.4} \\ W_n=10^{7.4} \end{gathered}[/tex]Similarly for the earthquake that happened near Woodburn Oregon in 1993 which had a magnitude of 5.6, the ratio of the seismic wave that occur is expressed as:
[tex]\begin{gathered} 5.6=\log (\frac{w}{w_o})_O \\ (\frac{w}{w_o})_o=10^{5.6} \\ W_o=10^{5.6} \end{gathered}[/tex]Taking the ratios of the seismic wave will give:
[tex]\begin{gathered} \frac{W_n}{W_0}=\frac{10^{7.4}}{10^{5.6}}_{} \\ \frac{W_n}{W_0}=10^{7.4-5.6} \\ \frac{W_n}{W_0}=10^{1.8} \\ \frac{W_n}{W_0}=63.096 \\ W_n\approx63W_0 \end{gathered}[/tex]This shows that the earthquake in North Cascades was about 63 times greater than the earthquake that happened near Woodburn Oregon in 1993
