[VẬT LÝ 12] Đại cương sóng dừng trên dây - Thầy Vũ Ngọc Anh

Hello everyone, welcome back to our lesson. Today, I will introduce a new song, which is the forest on the rope, followed by the intersection song that I have learned. And after the forest on the rope song, we will learn the sound song, which is the last song of this musical scale, to start a new scale, which is the electric scale. Today, we learn the forest scale. I evaluate that in this second scale, which is the sound scale, the forest scale is the easiest. But it's easy, it's the easiest, but it still has some difficult qualities that if you don't pay attention, you can still forget and make mistakes. And the theory of this song is very little, mainly it is an exercise in quality and formula only. So what is the forest on the rope? What does the forest mean? What is the forest? Stop, stop, right? So why is this forest on the rope after the intersection song? Remember, this forest on the rope is accompanied by some theoretical definitions of the intersection. Later, you will know why it is a forest. Why does it mean a forest? Later, I will explain the clear meaning of the word forest. What is a forest? The day before I learned the intersection song, I knew one of the important qualities of the musical scale is the intersection. To mention the rope, we have to mention the intersection. And when it comes to the rope, people also mention a very important quality, which is the reflection of the rope. It's like you shoot a ball into the wall, right? Shoot the ball into the wall, the ball turns back. That's reflection, right? That's called reflection. So a scale is the reflection of the rope. The reflection of the rope. Yes, the rope has the property of reflection, intersection. Later, when you learn it, for example, the light bulb is still flickering, still flickering. A is the fixed point of reflection. Let me show you an experiment. Look at this. This is a rope, right? A rope. Look at it. This head is the hand of the person holding it, right? It is stimulated, right? Stimulated to create a wave on this rope. And look at this. When people swing once, right? It's like you hold a swing, you swing once, right? It creates a wave top. And that top will spread over this rope. This is the wave or single wave, right? The wave will spread over this rope and reach that fixed point, right? It will reach that fixed point. And after this wave, it's called the next wave, reaches the fixed point, based on experience, based on experience, I know. The next wave is reversed. Can you see the video clearly? Remember? It's reversed. It's called a reflection wave. Reverse. Compared to the next wave. Because when it hits the fixed point, the fixed point makes the next wave reverse. It becomes a reflection wave. And these two waves are reversed. Here. Can you see it clearly? Here. This is a rope. It has the nature of a swing, right? This head is stimulated to make it move, right? By swinging once, it creates a wave, that is, a wave top. And I know, the wave is the spread of state. This wave top will spread to the fixed point, which is waiting over there, right? And when it hits the fixed point, the wave is reversed. It becomes a reflection wave. The reflection wave is reversed. Can you see the picture clearly? Okay. So here we say, at the fixed point, the reflected wave and the next wave have the same frequency, the same frequency, the same wave, but reversed at the reflected point. It still maintains the frequency, as if the energy does not decrease. The frequency must be maintained. The frequency is the nature. It will not change. Right? The same wave. Because you see, in an environment, the speed is the same, the frequency is the same, the wave is the same, but based on the nature, based on the nature, you know, right? The wave top will turn back. So what do we say? The reflected wave and the next wave are reversed at the reflected point. Okay. Let's go to B, which is the free reflection point. You just know that at the fixed reflection point, the reflected wave and the next wave are reversed based on the nature. They are reversed back. So what about the free reflection point? I will continue to experiment. This head is still stimulated by one hand. It creates a wave by shaking once. Right? There will be a next wave coming and the other point is not held tight anymore. It releases freely. Look at this. I observe the phenomenon. The next wave and the reflected wave are reversed together. It is not reversed. Right? This is our shape. This is a string. The other head is not held tight anymore. It releases freely. When a wave reaches the free head, the reflected wave will turn back. It is not reversed. Of course, the next wave and the reflected wave are reversed together. It is obvious that they are reversed together. The name of the phenomenon is the reflected wave and the next wave. Right? When you pull the wall, the wall is turned back. Right? The reflected wave goes and the reflected wave comes back. They are reversed. But we are looking at the top. Right? The top is still on the string. And what do people say? At the free reflected point, the reflected wave and the next wave still have the same frequency, the same frequency, the same wave and they are mixed together at the reflected point. In other words, the top of the wave is not reversed. People say it is the same as the beginning. That is, they are mixed together. At the free reflected point, the reflected wave and the next wave are mixed together. So, you have to understand what is the phenomenon of a string wave. You have to understand. There will be a lot of waves. Most of the times we do it. More and more of the wave will go to the reflected point. And the reflected point returns the reflected wave. At that time, many surrounding waves will come and the reflected wave will go back and forth. Right? Then the wave and the reflected wave are mixed together. The next wave and the reflected wave will be mixed together. More and more waves come and the reflected wave will go back and forth. The two waves it will intersect with each other and here is the intersection on the same side that is the side of the wire so you know, the forest is the phenomenon the intersection between the forward and the reverse on the same side have you learned the intersection? for example, the intersection on the water surface is the meeting of two forward waves right? here are also two waves because the intersection must have two waves but what are the two waves here? is the forward wave and what is the reverse wave? do you understand the word forest? because the forward and the reverse intersect so it will stop do you understand? it stops the word forest like that the forward wave and the reverse wave intersect intersect and stop the energy is retained there and it does not transfer anymore with the normal wave you know, the transfer of the wave is the transfer of the state transfer of the energy right? but with the forest wave it is retained it intersects it is retained and when there is a forest wave the energy is not transferred anymore it stops in one place do you understand? but in the process of creating the forest wave there is still energy transfer but when there is a forest wave there is no energy transfer anymore do you understand? the energy is retained it stops in one place so it is called the forest wave and invite you to watch a video of the forest wave phenomenon forest wave experiment with foreign videos let's go you have just watched a very good video about the forest wave experiment people also maintain a fixed point and I see the reverse wave is opposite to the forward wave at the fixed point and when people swing the rope many times create many waves there are many reverse waves and the forward and forward waves collide to create the forest wave phenomenon do you understand? so the reverse wave is the forest wave we study it more carefully than the experiment look at this this is a simulation of the forest wave phenomenon do you understand? look at this remember that we only have a rope do you remember? we only have a rope and the blur look at this that is the phenomenon of scattering images on the screen remember like a fan when it turns too fast you can't tell where is the real fan and where are the images on your screen because an image is born and gone it still lingers on your eyes for 1 in 10 seconds do you understand? so we look at the blur but in fact, there is only one rope and it is moving too fast we can't see it at any specific location here I have drawn it clearly for you this is the forest wave look at this the wave does not spread anymore but the particles are retained the energy is retained in one place do you understand? for example, you have to understand this in the machine wave any point can become a wave top because when the top hits it it goes to the top look at this in the forest wave there are points that stand still look at the second image the image in the middle the point in the middle it stands still it doesn't move and it can't go to the top at this moment the energy is retained and is dissipated here the reflection wave and the next wave are mixed dissipate each other energy each other do you understand? so that point has no energy so it stands still the third image there are two points that stand still look at the middle in the middle there are two points that stand still I don't talk about the two points at the same time we will analyze it later do you understand? you have to understand this in the forest wave image there are points that move very strongly look at the first image the point in the middle of the wire right? the first image the point in the middle of the wire it moves very strongly its amplitude is very large right? and the second image you know there is a point it doesn't move right? so the point that moves very strongly is the next wave the reflection wave it interacts with each other but it increases each other right? it doubles up do you understand? it becomes a very strong point but the reflection wave until it intersects intersects then it disappears it remains empty those points it doesn't move do you understand? so there will be a forest wave image like this this is a forest wave image on a wire remember we only have one wire and the others are just images of you on the screen there are points that move very strongly people call it live belly belly that is, the point with the largest amplitude belly live belly is the point that moves the furthest compared to the equilibrium position equilibrium position is the position where the wire is horizontal do you understand? live belly is the point with a very large amplitude it is called live belly and the point that doesn't move a little looks like this do you understand? this is called the live button do you understand? live button is the point that doesn't move of course and I know from this button to that button people call it a wave on the wire there are many other points that also move but will be smaller than the amplitude of the live belly live belly is the largest amplitude do you understand? and between two live buttons people call it a wave do you know the rice ball? people pinch both ends right? pinch both ends it's called a wave right? here it is a wave is the distance between two consecutive live buttons so here look at this the forest wave is the phenomenon intersection between the next wave and the reflection wave on the same plane intersection so the question is what are these two waves? the next wave and the reflection wave are intersecting on the same plane and later you'll see the forest wave is used to measure the speed of the wave on the wire the forest wave is used to measure the speed of the wave on the wire and later you'll see and the point that doesn't move button that is the next wave reflection wave intersection when they are intersecting but they intersect the point of intersection of a point and a point becomes a point of course What is this point of intersection? It's not moving. At the fixed point, is that point moving? We will analyze in 2 directions The fixed point means its mathematical meaning What is fixed? Of course it is not moving The fixed point is not moving The fixed point is a point of intersection But why is it not moving? Let's prove it The point of intersection of a point and a point is not moving The point of intersection of a point and a point is not moving The point of intersection of a point and a point is not moving The point of intersection of a point and a point is not moving The point of intersection of a point and a point is not moving The point of intersection of a point and a point is not moving The point of intersection of a point and a point is not moving Let's go deeper into the forest Let's analyze This is a rope with a forest and I draw 3 waves Remember that each wave is the distance between 2 continuous nodes Do you understand the word wave? Wave is the distance between 2 nodes A grain of rice Here are 3 waves How many? Many of you will answer 6 No, it's only 3 This is a rope One grain below, one above and one below We have 3 grains How many nodes? 4 nodes 3 grains, 4 nodes 2 nodes make 1 grain What is the distance between 2 continuous nodes? The distance between 2 continuous nodes is half of the wave on the rope This is based on the forest process But we will not learn about the forest process In fact, the forest process is quite similar to the cross-process Because the forest process is cross-process If you try to write, you can write But it's not the same The distance between 2 continuous nodes is lambda over 2 And here people call it the length of a grain One grain is lambda over 2 So 2 grains are 1 lambda And 3 grains are 3 lambda over 2 Or One grain is a sine They correspond to each other very well The sine is the path through the grain So 2 continuous nodes is lambda over 2 So from one node to the adjacent grain is lambda over 4 Or 2 continuous nodes is lambda over 2 Look, 2 continuous nodes is lambda over 2 But remember This is the distance along the horizontal axis Because the grains move up and down So the actual distance must be a diagonal line from one grain to the other But here we calculate the distance along the horizontal axis So 2 continuous nodes is lambda over 2 Or from one node to the adjacent node is lambda over 4 Got it? Next, we have the following statement The points belonging to the same wave move in the same direction The points belonging to 2 adjacent waves move in the opposite direction Why is there this? Of course, it's still from the forest process But we will not write the forest process We will look at it It's very easy The first wave The points will move up and down up and down Right? You know mechanical motion The points moving up and down are all like that So what are the points? They are mixed In other words, in a wave the points always move in the same direction Remember that in the same wave the points move in the same direction But look at this Why in 2 adjacent waves the points move in the opposite direction No need to prove Look at the second picture 2 adjacent waves 1 wave, 1 point moves up the other point moves down When 2 points move in the opposite direction Observe When 2 points move in the opposite direction the points move in the opposite direction See? Now look at the next picture There are no more waves Look at the third picture There are 3 points 1 point, 2 points 2 points move in the opposite direction 1 point and 3 points move in the same direction Look at 1 point and 3 points 2 points move in the opposite direction When the two stomachs are up together, the stomach in the middle is down to prove that the stomach in the middle is upside down. So, in total, I draw 6 lines. We have 6 lines. Look at this. The numbers are 1, 2, 3, 4, 5, 6. But the lines 1, 3, 5 are odd numbers. These lines will be mixed together. Or 2, 4, 6 will be mixed together. But what about 1 and 6? What is 1 odd and 1 even? Opposite mixed together. Or 2 and 5, right? 1 even and 1 odd are also mixed together. In total, when we make it bigger and wider. OK. Done. We draw 3 lines. These are 3 special points in a wave. And this is the most difficult part of the forest wave. You have to memorize and learn this. We have to react very quickly. With these 3 special points. For example, in the circle of garbage in the engine room, right? You have learned from the teacher. You are very familiar with 3 angles. 30 degrees, 45 degrees and 60 degrees. You practice a lot until it becomes your reflex. Right? In the forest wave, there are 3 special points. They correspond to angles 30, 45 and 60. But it will be more difficult to remember. Because it is in a space. But the teacher wants you to remember this part. This is a very important part. To learn the forest wave, you just need this. Just remember that you are good at the forest wave. Here. This is a very large wave. There are a lot of special points in it. This wave has a B point. And a wave has a length. See? How much is it? Lambda over 2. The wave has 2 consecutive points. Lambda divided by 2. Next, you know. We will have a reflected wave. It has a frequency. It is A. Why do we have to calculate this frequency? Because we know that the length is lambda over 2. How much is the width? The width is lambda over 2. How much is the width? Look at this. The forest wave is the intersection between the reflected wave and the incoming wave. In the same direction. Right? So the incoming wave and the reflected wave have to stimulate it. Right? Stimulate it with a frequency of A. Let's try to see. What is the frequency of the belly? Or just A? Come on. The belly is the interaction between the incoming wave and the reflected wave. They are mixed together. They are enhanced. A meets A. Enhanced. So what does it become? It becomes 2A. It is like the calculation to sum the interaction. Right? The forest wave is the intersection. The intersection is the sum. That is, the forest wave is the sum of the interaction. The reflected wave is mixed together. What does it become? 2A. Right? And of course, the node is A minus A. It is 0. Right? The node is not interacting. What is the frequency of the belly? It is 2A. Here. The frequency of the belly is 2A. So I will say it. I won't write it down here. But you will know. What is the frequency of the belly? The frequency of the belly is 10A. Look. This belly point interacts around the equilibrium. The equilibrium is horizontal here. See? The belly point interacts up and down. Right? So its frequency is 10A. The frequency of the belly is 4A. The length is lambda over 2. The frequency is 4A. The belly point is very strong. Very strong. Up and down. So what is the frequency of the belly? 4A. Look. I will divide it again. The frequency of the belly is 4A. The length is lambda over 2. The frequency of the belly is 4A. The length is lambda over 2. The frequency of the belly is 4A. Look. I will divide it again. The length is lambda over 2. The frequency of the belly is 4A. The length is lambda over 2. The frequency of the belly is 4A. The length is lambda over 2. Speed does not change in one environment. One environment is the string. Speed does not change. But if you change the frequency, Speed does not change. Frequency does not change. It makes lambda change. If lambda changes, it leads to the fact that if L is divided by lambda over 2, and there is no original number, then there will be no wave on the string. So this frequency line is a rule. You have to give up that frequency. You have to give up that frequency to have a wave on the string. The first thing to do is with two fixed ends. I know. With two fixed ends, the length of the string is L divided by K times lambda over 2. The length must be a number of times of lambda. And remember this. The length of the string cannot be changed. It is a fixed string. The length of the string cannot be changed. But that lambda can be changed by changing F. Changing F. Because V does not change. But lambda can be changed by changing F. What can we get? L is equal to K times V over F. Because lambda is V over F. So L and V cannot be changed. V is a number in an environment. And L is the length of the string. It is fixed from the beginning. So we get F. F is equal to K times V divided by 2L. See? F is equal to K times V divided by 2L. V is a number. L is a number. So V divided by 2L is a number. Right? So we just try to change F by changing the length of the string. OK? Look at this. In the first case, the smallest number to have a string is equal to Kmin. Kmin is equal to 1. K is the original number. It cannot be equal to 0. If it is equal to 0, there is no number. It is unreasonable. See? Kmin is equal to 1. Now Fmin is F0. See? F0 is the smallest number to have a string. See? F0 is the smallest number to have a string. It is V divided by 2L. This is very important. This is the smallest number to have a string. So we have to minimize this number. It is V divided by 2L. Then the string will have a string. And now the string has a string. With how many strings? K is always the number of strings. K is equal to 1. So what do we have? One string. At this moment, there is one string. So what do we do? The string has a string. It is exactly one string. But with this F0, for example, F0 is equal to 50Hz. See? If I have 51Hz or 52Hz, there is no string on the string. See? And I set F0 to be V divided by 2L. Then I get any number must be equal to the whole F0. Because F0 is equal to V divided by 2L. That is, the smallest number to have a string is 50. Then what is the next number? 100, 150, 200. See? But 220 is not enough. So what is it? K times F0. You know, K times F0 must be the whole time of the smallest number. Here. Continue with K divided by 2. The next number to have a string must be 2F0. At this moment, K divided by 2 has how many strings? There are 2 strings. There will be 2 strings on the string. Remember? Remember that we increase F, so that lambda decreases. Lambda decreases, so that there will be more strings on the string. At this moment, there are 2 strings on the string. And the length of the string is still unchanged. Remember? Continue with K divided by 3. F3 is equal to 3F0. Because F is equal to K times F0, the whole number of the smallest number. Remember? At this moment, K divided by 3 has 3 strings. There are 3 strings on the string. 3 live strings are living on the string with 2 fixed numbers. So, the number to have a string on the string, is F0. 2F0, 3F0, and so on, up to KF0. It is the whole number of F0. F0 is the smallest number to have a string, which is V divided by 2L. If you forget F0, V divided by 2L, you are screwed. Remember? The smallest number to have a string is V divided by 2L. I put it in. Got it? V divided by 2L. Remember? So, what is this number? It is the whole number. So, 2 whole numbers divided by F0. 2 whole numbers divided by 1F0. Got it? 2 whole numbers divided by 1F0. See? 3F0, 2F0, divided by 1F0. So, 2 whole numbers to have a string divided by 1F0. For example, from F0 to 2F0, increased to 1F0. Increased to 1. From F0 to 3F0, increased to 2F0. Got it? 1 to 3, increased to 2. Right? Increased to 2F0, increased to 2. So, 1F0, 2F0, increased to 2. Got it? Increased to 1F0, increased to 1. Decreased to 1F0, decreased to 1. This F0 means 1. But here is the thing. Increased to 1F0, increased to 1. But, for example, increased to 1F0, increased to how many? This is complicated. Increased to 1F0, increased to 1. Many of us will think increased to 1, increased to 2, so, you are wrong. The increased to thing is different. Increased to 1, increased to 1. Look at the first picture. The second shape has two sticks, but only has a few buttons. 1, 2, 3. The second shape has three buttons. Remember, increase one stick means increase one button. Don't make a mistake. Be careful. There will be some mistakes here. The small b part is a free head and a fixed head. The last part. A free head and a fixed head. You know, the length of the wire is L, right? K lambda over 2. But the free head has to add lambda over 4. It's half. So here, I group lambda over 4 out. The purpose of grouping lambda over 4 out is very good. It creates a rule inside. 2K plus 1. What is that number? 2K plus 1 is an odd number. See? 2K plus 1 is an odd number. And now I know that lambda is equal to V over F, right? So it will be equal to 2K plus 1 times V over 4F. Remember, lambda is equal to V over F. Got it? What is F equal to? F is equal to 2K plus 1 times V over 4L. 2K plus 1 is an even number. Got it? F is an even number of V over 4L. Now, how many times does K min? K min must be equal to 0. Got it? At this point, we don't need 1. 0 is already min. Because F is still 0. At this point, F0 is the smallest number for a wire. It is V over 4L. The smallest number for a wire is V over 4L. Got it? The other one is V over 2L. But this one is V over 4L. At this point, how many times does K min? K is an even number. If K is equal to 0, it means there is no even number. Got it? There is no even number. At this point, look at this picture. Right? It has both a fixed and a fixed end. There is no even number. What is an even number? It is between 2 nodes. Got it? As you know, an even number is an even number times F0. F is equal to 2K plus 1 times F0. It is an even number times F0. 2K plus 1 is an even number. Instead, the next K is from 0 to 1. Right? Instead of K1, 2K plus 1 is equal to 3F0. Got it? The next number for a wire is 3F0. Got it? At this point, K1 has 1 node. What is the picture like? It is exactly like this. Got it? 1 node and half a node must be left out. Similarly, for K2, F2 is equal to 5F0. It must be an even number. 1F0, 3F0, 5F0. At this point, the wire has 2 nodes. What is the picture like? Got it? The number of nodes is increasing. So, what is an even number? Its even number is an even number times F0. F0, 3F0, 5F0. In total, it is 2K plus 1F0. It is an even number times F0. And as you know, two even numbers are divided into different units. For example, in A, there are two fixed nodes. Got it? So, it is an even number times F0. Two even numbers are divided into different units. But here, there are two even numbers divided into different units. Got it? So, two even numbers to have a wire must be divided into 2F0. Remember, it must be 2F0. Got it? And increasing 2F0 is an even number. Increasing 1F0 is nothing. For example, 3F0 plus 1F0 is 4F0. There is no even number. Because even number must be an even number times F0. And F0 is divided into 4L. Don't get me wrong. It is divided into 2L. Two fixed nodes must be divided into 2L. But one fixed node, one free node must be divided into 4L. OK. That's all for the 5th part. Let's move on to the 6th part. That is the important points when solving even numbers. The last part, 6th part, has 3 important points. There are always 3 important points in learning. Got it? The first note, note 1. Got it? What is it? The time between two consecutive lines is half a century. Why do we know this? Look at the figure. During the interaction, right? Look at the point B. In a wave, point B is the most observable point. Because it is the most prominent point. It has the largest frequency. Got it? It goes up and down, up and down. The points in the same wave are always mixed together. If B goes up, other points go up. If B goes down, other points go down. Sometimes, they go through the equilibrium position. Look at the figure. Stop and look at it. Got it? Sometimes, the lines are parallel. Got it? So people often ask, how long is the time between two consecutive lines? Got it? Let me tell you. In order for the lines to be parallel, the point B has to go through the equilibrium. Got it? Parallel lines when B goes through the equilibrium. So parallel lines twice in a row, B has to go through the equilibrium twice in a row. Right? A point that goes through the equilibrium twice in a row, is 1.5 meters. Got it? So, if you multiply it by 3 times, T3 is 2.5 meters. 4 times in a row, is 3.5 meters. Because 2 times is only 1 meter. So, 3 times is... Sorry, 2 times is 1.5 meters. 3 times is 2 times 1.5 meters. And multiply it by n times in a row, the parallel lines are... n minus 1 is 1.5 meters. 2 times in a row, parallel lines is 1.5 meters. That's the first point. Let's go to the second point. This point is difficult. Pay attention. Look at this. In a wave, there are always two points with the same amplitude. And that amplitude is smaller than the amplitude of the point B. Look at this figure. In a wave, look at this. Point B is the point with the largest amplitude. For example, point B has an amplitude of 4. You have to remember this. What is the amplitude of the point B? The amplitude of point B is 8. The amplitude of point B is 4. The amplitude of point B is 8. Let's imagine. For example, the amplitude of point B is 4. And the amplitude of point B is the highest. The other points will be parallel to each other. Two lines on both sides. You see? They are parallel to each other. And there are always two points with the same amplitude. You see? These two points have the same amplitude. What is the same amplitude? A smaller number than 4. So, the amplitude of point B is 4. Right? So, in this figure, there are 6 points. The amplitude is 3. Because there are 2 points for each line. There are 6 points for 3 lines. You see? In one line, there are always two points with the same amplitude. And the amplitude is smaller than the amplitude of point B. You see? Point B is the highest. And it is parallel to each other. It is parallel to each other. You see? There are two points with the same amplitude. Let's move to the third point. Let me show you the last point. This is the most important point. This point has been in the college entrance exam. And many colleges have taken this point. It is very important. There. The third point is very important. It has been in the college entrance exam for 10 years. You see? Here. On the string, there are points parallel to each other with the same amplitude. Now, you think about the string with the forest stream. Which points are parallel to each other? Look at this figure. This is a string with a forest stream, right? Look at it. Look at it with your eyes. You see? Which points are parallel to each other? Which points? You think of them as parallel to each other, right? The points are parallel to each other. But you omit the notes. Why do you remove the notes? You omit the notes because they are not dynamic and often violate the following condition. They are parallel to each other, right? The points are parallel to each other. You omit them. But the notes are not dynamic so don't use the notes. You see? The first case you have to know is the points are parallel to each other but have the same amplitude. They are lines. You see? How many points are parallel to each other? Lambda divided by 2. The first case is the waves. The waves have the same frequency. The same frequency is 2A, double the frequency of the next wave. Got it? The frequency of the wave is 2A. And how many grams is the wavelength of the wave? Lambda divided by 2. According to the equation, Lambda divided by 2 is half of the wavelength. A1 divided by 2A is minus 1. D1 divided by lambda divided by 2. But what about the second case? Can you guess what it is? Get smarter. How do the McNuggets match? They are pretty similar. Right? How do they match? McNuggets are all similar. There is the copying finger there. Got it? The Nuggets and the McNugget coefficients are similar. This is how the belly is divided into 2. The second point is the center of the belly and the belly button. It's also divided into 2. Let's try to calculate the lambda divided by 4. The center of the belly and the belly button is the special point. It's the point P in the 3 special points. Remember, the center of the belly and the belly button will have an angle of angle of 2. The angle of the belly is 45 degrees. The angle of the belly button is angle of 2. And these points will be divided into lambda divided by 4. Because the center of the belly and the belly button is lambda divided by 8, the 2 points will be divided into lambda divided by 4. Can you see the 2 points? The center of the belly and the belly button is the point P. They will be divided into lambda divided by 4. This is very important. The 3rd point is important. And to distinguish these two cases, you know, A1 is bigger than A2, right? Because the volume will have a magnitude greater than the center of its volume, right? Next, what is D2 equal to? 1 half D1 or D1 times 2 times D2 In short, A1 is bigger than A2, D1 is also bigger than D2 And D1 is equal to what? Equal to 2 times D2 A1 is equal to what? Subtract 2 times of what? A2 Remember, this third point is very important We have learned the points in the same way And the same magnitude is the center of the volume and the center of the volume and the volume Are you done? OK So we have finished the theory of forest waves Here are all the theories for you And there are also a lot of solutions in it If you mention forest waves, just remember that Forest waves are the intersection between incoming and outgoing waves in the same direction There is nothing else, right? But I have shared with you a lot of theories, a lot of properties And there are also methods to do exercises This forest wave, it is not difficult to solve the exercise In Beeline, it takes only 1 hour to solve the exercise You will learn very well about forest waves Forest waves are not difficult It's different from intersection Intersection, you see, the exercise is extremely difficult Because it is an intersection on the surface of the water You have to solve a lot of straight lines You see But forest waves are on a string So the exercise is not too much Just give you 3 points But it is difficult in one place It is difficult in forest waves This is the part of the increase in the live stream We will study carefully, you see About forest waves Forest waves are difficult to solve But solving forest waves is extremely easy Forest waves must be solved on a string is difficult And I wish you after this video You will understand more than 80% of the theory that I teach you The remaining 20% we will understand more deeply Understand more in the live stream before the exercise A lot of exercises Goodbye