Question

Can someone pleas help, and explain this?

Answer 1

a) Chicago: 3 min, Savannah: 4 min, Seattle: 4 min

b) Chicago: 1800 km, Savannah and Seattle: 2600 km

c) Using the intersection between the 3 circles

Explanation:

a)

In this part, we want to find the difference in arrival time between P waves and S waves for each city.

For Chicago, we have:

- P waves arrival time: 3 min, 40 s

- S waves arrival time: 6 min, 40 s

So the difference in arrival time is:

$\Delta t = 6 min, 40 s - 3 min, 40 s = 3 min = 180 s$

For Savannah, we have:

- P waves arrival time: 4 min, 50 s

- S waves arrival time: 8 min, 50 s

So the difference in arrival time is:

$\Delta t = 8 min, 50 s - 4 min, 50 s = 4 min = 240 s$

For Seattle, we have:

- P waves arrival time: 2 min, 55 s

- S waves arrival time: 6 min, 55 s

So the difference in arrival time is:

$\Delta t = 6 min, 55 s - 2 min, 55 s = 4 min = 240 s$

b)

Here we want to find the distance of each city from the epicentre of the earthquake.

In order to do that, for each city we have to take the difference in arrival time between P waves and S waves, look at the corresponding value in the graph (y-value), and then check what is the corresponding value on the x-axis, which gives the distance from the epicentre.

For chicago, we know that

$\Delta t = 3 min$

Interpolating the graph, we see that a time difference of 3 min corresponds approximately to a distance of 1800 km from the epicentre.

For Savannah and Seattle, we know that

$\Delta t = 4 min$

Interpolating the graph, we see that a time difference of 4 min corresponds approximately to a distance of 2600 km from the epicentre.

c)

The information from 3 different cities can be used to determine the exact location of the earthquake's epicentre.

In fact, we now know the distance of the epicentre of the earthquake from each city.

If we only have this information from 1 city, we would only be able to draw a circle with centre in the city and radius equal to the distance from the epicentre, and each point along the circle would be a potential location for the epicentre.

If we had informations from 2 cities, we could draw 2 circles each centered on one city, and we would have two intersections between the two circles, which would give us 2 potential locations of the epicenter.

Instead, if we have 3 cities, we can draw 3 circle, and there is only 1 point of intersection between the 3 circles: that point is the location of the epicenter.