Good afternoon everyone, I am Sir Jude and today I will be discussing the only topic that we tackled this week, epicenter to Yangtze River. So let's have our first sample problem. An earthquake shook the Philippines.
Seismic stations in Cebu, Palawan, and Batangas were the first to detect body waves. Locate the epicenter where the earthquake originated. So remember, in the problem set that I gave you, we start first with local, for example, using three cities in the Philippines.
So in the table first, you are given the time arrivals of the P wave and the S wave, both of which are considered body waves. So why doesn't it include the Love wave and the Rainy wave? That's because both PNS waves as body waves, they arrive earlier and faster compared to the surface waves which arrive later and slower.
So Cebu, here are the P wave arrivals for the following cities. For Cebu, it's seven seconds. For Palawan, it's three seconds.
And for Batangas, it's only one second. So from the P wave arrival alone, we can conclude that of the three stations, The first station which detected the earthquake or the seismic waves is Batangas because in only one second, it already felt and recorded. But the third and last station of these three to record or detect the seismic waves is Cebu because it took seven seconds. For the S-Wave Arrival, it's also in seconds. So Cebu it's 103 seconds, for Palawan 63 seconds, and Batangas 41 seconds.
So before we consult our map let's first finish the table of values here by starting with land time okay. Okay, for a while. Ayan.
So, to get the lag time, because time is the first measurement we detect using the arrival of the P and S waves, no? So, to get lag time, we subtract the time of arrival of the S wave and the time of arrival of the... e-wave. So for Cebu, we have 103 seconds minus 7 seconds that will give you 96 seconds. For Palawan, we have 63 seconds minus 3 seconds.
was 60 seconds. Lastly, for Batangas, you have 41 seconds minus 1 second was 40 seconds. Alright, so, log time alone cannot effectively determine the exact location of the earthquake's epicenter.
We need the distance of the following stations from the epicenter in terms of kilometer and to obtain the distance from the epicenter we will use a different formula. Okay so when it comes to distance we're going to multiply the lag time in seconds by a constant 12.5 kilometers per second. Now, this value, 12.5 kilometers per second, is a constant. So every time that we compute for distance, that's the number that we multiply alongside the flat times.
Now, I have no idea why it's 12.5 kilometers per second. I only relied on the module that grade 10 students have been using. And it's not specified how it might reach 12.5 kilometers per second. So let's just stick with this one.
Anyway, in real life, we cannot pinpoint exactly where the epicenter is. This is just an approximation. So using the lag time we just calculated a while ago, the distance of Cebu from the epicenter is 96 seconds times 12.5 kilometers per second. it will give you 1200 kilometers.
For Palawan, you have 60 seconds times 12.5 kilometers per second giving you 750 kilometers. And lastly for Batangas, you have 40 seconds times 12.5 kilometers per second. That will give you 500 kilometers.
So what is the significance of computing the distance from the epicenter? So from the three stations, we start with the wall that is nearest to the epicenter. according to our calculations, Batangas because it is only 500 kilometers.
And the one that is farthest from the epicenter is Cebu, which took 1,200 kilometers. Alright, so later we will find out why it is very important for us to calculate the distance from the epicenter. But since we were going to use a map, we cannot use all values in kilometers in our map because our map is printed, I ask you, in just a bond paper whether you printed it in A4, short or long. So the only difference in paper is in centimeters.
That's why we have to scale these distances using another formula. So this is our last set of computation. For the scale distance, we will divide the distance from the epicenter by 100 kilometers per centimeter. So technically, we're really done with the computation and distance from the epicenter. We're just scaling the distance so that it fits the papel that you're drawing on the screen.
Alright, so starting off with Cebu, you have 1200 kilometers divided by 100 kilometers per centimeter that will give you 12 centimeters. For Palawan, you have 750 kilometers divided by 100 kilometer per centimeter that will give you 7.5 centimeters. And lastly for Batangas, you have 500 kilometers divided by 100 kilometer per centimeter and it will give you 5 centimeters.
Okay so because scale distance is the last set of calculations that means we have already computed the table you are now ready for your epicenter. I just erased all the writings, online writings I did. So, let's go to our map. So, I want... demonstrate to you how to use a compass, how to measure the length of the circles using a ruler, and how to draw a circle.
Because we already did that yesterday and this morning. So this is what we expect the look of the circles representing each how far the station is from the expected epicenter. So Cebu whose radius is 12 centimeters is represented by a red circle. So it is the largest of the three. While Palawan, whose radius is 7.5 centimeters, is represented by the colored green circle.
And Batangas, whose radius is 5 centimeters, is represented by the blue circle. I used different color codes for you to differentiate and distinguish one city from the other. Okay, so now since the title of our... Lesson is epicenter triangulation.
It's now time to find the actual epicenter of the earthquake. And the epicenter is actually the point where the three circles intersect. So the one that I marked with a star is the epicenter of the earthquake.
Okay, now so some of you when you drew the circles, a few of you were able to determine the exact location of the epicenter because the three circles actually did meet at exactly one point. While most of you, while I accepted your drawing, there are slight spaces, slight movements, or rather deviations from the ones that are actually designated for your output to look like. And that's fine because not everybody is perfect. You are human beings.
Not everyone can draw. circle. The others used compass for the first time. But I'm actually happy that this morning, most of you were able to adjust really fast and your performance in drawing circles improved better than yesterday.
So practice until you got it correct. And when it comes to compass, it's either you follow the compass or you make the compass stationary, the map will follow you. Either way, both will yield you the results. Alright, so here are some of the follow-up questions.
So number one, which station is the nearest from the earthquake's epicenter? So that station that is nearest from the star is none other than Batangas. Okay, second question, which station is the farthest from the earthquake's epicenter. So yung pinakamalayo sa epicenter is none other than Cebu.
Third question, which station will be the least affected by the earthquake and why? Okay so pagsasabi natin least affected by the earthquake, siya yung nakakakamdam ng mahinang impact ng lindol. And mahina ang impact ng lindol kung malayo ka sa epicenter. That's why that station will fall under city.
And finally, which station will be the most affected by the earthquake and why? So the station that will be most affected by the earthquake is the one nearest to it. Kasi masyadong malakas yung pag-inip.
Therefore, medyo malapit ka sa epicenter. So ang pinakamalapit among the three is none other than Batangas. Alright, so once you're done, plotting the three circles and the epicenter, you're basically done with epicenter triangulation. Alright, so here are some of the follow-up questions for day one. So you might notice, why are there three circles in the epicenter triangulation?
Why do we use three stations? So some of you answered, sir because it's triangulation and the prefix for triangulation is tri and tri means three. So yeah, well, that's it. But there's a deeper reason why we use age stations.
We cannot use only one, and we cannot use only two, and more than three is already exhausting to make. Imagine drawing four circles and you only have 40 minutes in our class. And some of you, admittedly, are slow in computing.
Even our calculations are simple. So I'm only gonna explain. why hindi pwede yung less than three. Okay? Eto.
So let's say for example you only have one circle like that. So in epicenter triangulation, we need circles overlapping and we cannot trust one circle only because what if it's just one circle but the epicenter is here, the star. So they don't meet, they don't match, it's too far, it doesn't belong. The epicenter is not even part of the or the station rather is not even part of the epicenter.
They don't even touch. Here's the disadvantage if we have two circles. First, what if the drawing you drew is from the zone?
And what if the other one you drew is Mindanao? The problem here is they don't have a point of intersection. You wouldn't be able to locate the epicenter of the circle. Here's another problem with two overlapping circles only.
If this is the only one, especially in this case, you have two intersections, you have two possible epicenters. So because we're only interested in one, having multiple epicenters will be confusing. And while that's also a problem if you have three circles, even more than three circles, how do I say this? I designed, we designed this problem so that using three circles, you will only have one exact epicenter.
Alright? And as you notice, hindi lahat ng station sabay-sabay nilang nasasagap ang primary waves and secondary waves. Meron na uuna, meron na uhuli, and mas maganda kung meron tayong isa na pumapagitna. So that's why we use three stations in epicenter triangulation.
Okay, next! Let me just erase my reds. Okay, second question.
What difficulties did we encounter in locating the exact location of the earthquake's epicenter? I am actually surprised and glad by the fact that you didn't answer the difficulties in problem solving. Because if we go back to earlier, you were just using simple and basic operations. So long time is just subtraction. distance from the epicenter is just multiplication and the scale distance is just division.
So even elementary students can perform those. We're not dealing with scientific notation, we're not using exponents, we're not using radicals, we're not using logarithms, and we're not using trigonometric functions. So all of our calculations are, to be honest, very easy for grade 10. But the difficulty is that what most of you encountered is number one, measuring the length.
Some of you are still confused about how to read the ruler, specifically some teachers. And that will be improved and refined through practice. Number two is holding the compass. Some people are really good at this. It really depends on the way you handle and manipulate the compass or the map, depending on the choice.
And number three, Unfortunately, there are people who, regardless of how good their work is, sometimes, the three circles don't intersect. Which is fine, right? But in our...
I specifically asked you to print using A4. And there are students who actually got the exact location of B, epicenter. But even if you don't, as long as it's close to the expected answer, that is fine with me. After all, in your performance tasks and long tests, to avoid lots of confusions and lots of questions, I will be the one to check personally.
Alright? So, this is where part 1 will end. And I will continue with part 2. And I will upload part 2 on a later date because we didn't meet 10 cars this morning because of the NK orientation. Until then, I'm Sir Jude.
and have a good day.