Question

travel time (min)
20
15
10
5
0
0 2,000 4,000 6,000 8,000 10,000
distance (km)
p wave
about how far does the s wave travel through earth in 13 minutes?
2,000 km
4,000 km
6,000 km
8,000 km

Explanation:

Step1: Identify S - wave line

The dashed line is the S - wave (since P - wave is solid orange). We need to find the distance for S - wave at 13 minutes.

Step2: Analyze the graph

First, look at the y - axis (travel time in minutes) and x - axis (distance in km). The S - wave line: when we estimate the slope or the relationship. From the graph, we can see the trend of the S - wave. Let's check the time - distance relation. At around 13 minutes, we can see the x - value (distance) corresponding to y = 13. Looking at the dashed line (S - wave), when y (time) is 13, we can estimate the x (distance). From the graph, the S - wave line at y = 13, the x is around 6000 km? Wait, no, wait. Wait, let's re - check. Wait, the P - wave is solid, S - wave is dashed. Wait, when time is 13, let's see the S - wave. Wait, maybe I made a mistake. Wait, let's see the options. The options are 2000, 4000, 6000, 8000. Wait, let's look at the S - wave (dashed) line. Let's take two points: at x = 0, y = 0; at x = 10000, y≈22? Wait, no, the y - axis goes up to 20. Wait, the S - wave (dashed) at x = 6000, y≈15? Wait, no, the problem is about S - wave. Wait, the question is "About how far does the S wave travel through Earth in 13 minutes?". Let's see the S - wave line. Let's find the slope. The S - wave: from (0,0) to (10000, let's say at x = 10000, y is around 20? No, the y - axis is up to 20. Wait, maybe the S - wave line: when y = 13, what's x? Let's see the options. Let's check the S - wave's time - distance. Let's see, if we look at the S - wave (dashed), at y = 10 minutes, what's x? At y = 10, x is around 4000? No, wait, no. Wait, the P - wave (solid) is slower? No, wait, P - waves are faster than S - waves. Wait, no! Wait, P - waves are primary waves, faster than S - waves (secondary). So the solid line (P - wave) should be below the dashed line (S - wave)? Wait, no, in the graph, the solid line (P - wave) is below the dashed line (S - wave), which means P - wave is faster (since for the same distance, P - wave takes less time). So S - wave is slower (takes more time for the same distance). So the dashed line is S - wave (slower, more time for same distance), solid is P - wave (faster, less time). So for S - wave (dashed), at time t = 13 minutes, what's the distance? Let's see the S - wave line. Let's take the S - wave: when t = 10 minutes, what's the distance? Looking at the dashed line, at t = 10, x is around 4000? No, wait, at t = 10, the S - wave (dashed) is at x = 4000? No, the P - wave (solid) at t = 10 is at x = 8000? Wait, no, I think I mixed up. Wait, let's correct: P - waves are faster, so for the same distance, P - wave takes less time. So the line with less slope (flatter) is P - wave (faster), steeper is S - wave (slower). Wait, no, slope is rise over run. So steeper slope means higher speed? No, speed is distance over time, so speed = x/t, so slope (t/x) is 1/speed. So a steeper slope (higher t/x) means lower speed. So S - wave (slower) has steeper slope (higher t/x), P - wave (faster) has flatter slope (lower t/x). So in the graph, the dashed line (S - wave) has steeper slope (higher t/x) than solid (P - wave). So for S - wave, t = 13 minutes. Let's find x. Let's see the S - wave line: when t = 13, what's x? Let's look at the options. Let's check the S - wave's time - distance. Let's take the S - wave: at x = 6000 km, what's t? From the graph, the dashed line at x = 6000, t is around 15 minutes? Wait, no, the y - axis is up to 20. Wait, the problem is asking for 13 minutes. So if at x = 6000, t is 15, then at t = 13, x is less than 6000? No, that can't be. Wait, maybe I got the waves reversed. Let's think again: P - waves are faster, so for a given time, P - wave travels more distance. So the solid line (P - wave) should be above the dashed line (S - wave) in terms of distance for same time? No, no: for same time, faster wave (P) travels more distance. So at time t, distance of P is more than S. So in the graph, for a given y (time), x (distance) of P is more than S. So the solid line (P) is to the right of dashed line (S) at same y. So at y = 13, the solid line (P) is at x =?, dashed (S) at x =?. Let's look at the options: 2000, 4000, 6000, 8000. Let's see, the S - wave (dashed) at t = 13, what's x? Let's see the S - wave line. Let's take two points: (0,0) and (10000, t≈22). So the equation of S - wave: t = (22/10000)x. So x=(10000/22)t. For t = 13, x=(10000/22)*13≈(454.5)*13≈5900, which is around 6000 km. So the answer is 6000 km? Wait, but let's check the graph again. The dashed line (S - wave) at t = 13, looking at the graph, the x - axis is 0 to 10000. At t = 13, the dashed line is around x = 6000. So the answer is 6000 km. Wait, but the options are 2000, 4000, 6000, 8000. So the correct option is 6000 km. Wait, but maybe I made a mistake. Wait, let's check the P - wave. P - wave (solid) at t = 13, x is around 8000? No, P - wave is faster, so at t = 13, P - wave would travel more distance. But the question is about S - wave. So S - wave, slower, so at t = 13, distance is around 6000. So the answer is 6000 km.

Answer:

6,000 km (corresponding to the option with 6,000 km, e.g., if the option is C. 6,000 km, then C. 6,000 km)