(II) P and S waves from an earthquake travel at different...

(II) $\mathrm{P}$ and $\mathrm{S}$ waves from an earthquake travel at different speeds, and this difference helps locate the earthquake "epicenter" (where the disturbance took place). (a) Assuming typical speeds of 8.5 $\mathrm{km} / \mathrm{s}$ and 5.5 $\mathrm{km} / \mathrm{s}$ for $\mathrm{P}$ and $\mathrm{S}$ waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 1.7 min apart? (b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

(II) $\mathrm{P}$ and $\mathrm{S}$ waves from an earthquake travel at different speeds, and this difference helps locate the earthquake "epicenter" (where the disturbance took place). (a) Assuming
typical speeds of 8.5 $\mathrm{km} / \mathrm{s}$ and 5.5 $\mathrm{km} / \mathrm{s}$ for $\mathrm{P}$ and $\mathrm{S}$ waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 1.7 min apart? (b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

Key Concepts

Seismic Waves

Seismic waves are energy waves generated by earthquakes or other sudden disturbances in the Earth’s crust. They propagate in different forms, including primary (P) waves and secondary (S) waves, each with distinct speeds and characteristics. Understanding these waves is fundamental to seismology as they provide crucial information about the source and internal structure of the Earth.

Propagation Speed of Seismic Waves

The speeds at which seismic waves travel depend on the properties of the materials they move through. P waves typically travel faster than S waves because they are compressional waves, while S waves, being shear waves, move slower. This difference in speeds is essential in determining the distance from the source of an earthquake, based on the time interval between their arrivals at a detection point.

Wave Arrival Time Difference

The time difference between the arrivals of different types of seismic waves at a seismic station is a key concept in locating earthquake epicenters. By measuring how much later the slower S wave arrives compared to the faster P wave, scientists can calculate the distance from the seismic station to the earthquake source using the known propagation speeds of the waves.

Triangulation in Seismology

Triangulation is a method used to pinpoint the exact location of an earthquake's epicenter. Since the time difference from a single seismic station only provides the distance from that station, multiple stations are necessary to form intersecting distance circles. The intersection of these circles, derived from time differences at three or more stations, helps accurately determine the earthquake's epicenter.

Transcript

00:01 So in this question, we have the earthquake, and in an earthquake, we have two kinds of waves.

00:08 We have the p wave, and we have the s wave.

00:13 And they travel at different speeds, and there's difference.

00:16 That's difference between when these two waves arrive or tell us where the earthquake happens, like where is the center of the earthquake.

00:27 So right now we're assuming that's typical speed of p wave is 8 .5 km per second and for s wave it's 5 .5 kilometer per second.

00:42 So we ask how far did the earth could occur if the station detects the arrival of these two waves to have 1 .7 minutes apart.

00:59 And the second question is is one station sufficient to determine.

01:04 The position, the epicenter.

01:06 So that is the question we can properly answer without doing part 8 right.

01:13 The answer will be no, and we can talk more about this when we actually continue it.

01:20 So firstly, they will put seven minutes apart.

01:24 So the distance delta x between the epicenter and the station is equal to v1 t1 and p22.

01:37 Because that's the distance traveled by the s wave.

01:41 So the quite, what we can call t wave number one, is wave number two.

01:47 I can also possess bst or ptp.

01:51 But anyway, it's just that the two waves have their all speed and travel at their all time, but they travel the same distance from the center of the earth's quick to the station.

02:02 So from these, we will be able to tell that, let's see, actually i will call s number one because it has a smaller speed.

02:21 So we have t1 because it has smaller speed it takes longer to arrive, equals t2 plus 1 .7 minute turn.

02:33 Let's try to use second, we time it by 60, to be 102 second.

02:43 So we have v1 times t2 plus 102 second, equals v2 times t2.

02:53 And by rearranging this, we get t2 equals v1 over v2 v2 times 1 or v2 second, which is 5 .5 kilometers...

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