Question

The magnitude, M, of an earthquake in relation to the seismicwaves, W, can be modeled by M=log(w/w0)is called the Richter Scale.In 1872, the North Cascades suffered its largest known earthquake ofmagnitude 7.4. How many times larger was this earthquake than theearthquake that happened near Woodburn Oregon in 1993 which had amagnitude of 5.6?

Answer 1

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;

$M=\log (\frac{w}{w_0})$

If in 1872, the North Cascades suffered its largest known earthquake of magnitude 7.4, hence;

$\begin{gathered} 7.4=\log (\frac{w}{w_o}) \\ (\frac{w}{w_o^{}})_n=10^{7.4} \\ W_n=10^{7.4} \end{gathered}$

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:

$\begin{gathered} 5.6=\log (\frac{w}{w_o})_O \\ (\frac{w}{w_o})_o=10^{5.6} \\ W_o=10^{5.6} \end{gathered}$

Taking the ratios of the seismic wave will give:

$\begin{gathered} \frac{W_n}{W_0}=\frac{10^{7.4}}{10^{5.6}}_{} \\ \frac{W_n}{W_0}=10^{7.4-5.6} \\ \frac{W_n}{W_0}=10^{1.8} \\ \frac{W_n}{W_0}=63.096 \\ W_n\approx63W_0 \end{gathered}$

This shows that the earthquake in North Cascades was about 63 times greater than the earthquake that happened near Woodburn Oregon in 1993