In the name of God, the Most Gracious, the Most Merciful. Peace, mercy, and blessings of God be upon you, our dear students. In this video, God willing, we will continue explaining the unit on vibrations and waves, specifically the third section, Wave Behavior. Before we begin studying this section, remember our lesson that the speed of a wave equals the product of the wavelength and the frequency. We mentioned that if we have the same medium, and if we change the medium to two different mediums, then if we have the same medium, the speed is constant, while the wavelength and frequency have a direct relationship. What does that mean? An inverse relationship? I mean that if the frequency increases, the wavelength decreases, and vice versa. However, if we have two different mediums, then the frequency remains constant, while the speed and wavelength have a direct relationship. That is, if the speed increases, the wavelength increases with it, and vice versa. So, my dear student, what does the speed of mechanical waves depend on? The properties of the medium through which a wave travels are the only factors; as long as it's the same medium, the speed remains the same. For example, the depth of water affects the speed of water waves, and temperature affects the speed of sound waves. Spring waves, however, are affected by tension, mass per unit length, and the medium itself. The medium is what changes the wave's speed. Here, we'll begin studying waves at their boundaries. Dear student, we have two examples. In the first example, we have two springs. The first spring is stiffer; we'll represent it by its slightly greater thickness. The second spring is less stiff. If a wave falls on the stiffer spring, we call this an incident wave. Part of it will be reflected, and part will be reflected. The part that passes through will travel in the same direction—it's transmitted—while the part that is reflected will be reflected, but with a smaller amplitude. So, where does the wave travel from? From a stiffer spring to a stiffer spring? This wave is called a reflected wave. A reflected wave is simply reflected, but with a smaller amplitude. Why is the amplitude less? Because part of the energy has been transferred to the other medium. So, can we draw the same amplitude? Yes, it can. Why? Because this is a different medium. That means the energy here is not equal to the energy here. The energy of the incident wave is partly transmitted and partly retained. What if we have the opposite, from a less rigid spring to a more rigid spring? Here, this incident wave is a cat. How will it be reflected and how will it be transmitted? The transmitted part will be transmitted in the same direction here, but the reflected part will be reflected, but it will be inverted. So here, from a less rigid spring to a more rigid spring, what happens to the reflected wave? The reflected wave will be reflected and inverted. What happens to the reflected wave? It is reflected and dripped, but with a smaller amplitude. Why? Because part of the wave moved. Notice here this diagram that we have in the writing. The incident wave is stinging, meaning part moved to the second spring and part bounced back. As long as it bounced in the same direction, then here it will be from more rigid to less rigid. But if it is reflected, it will be from less rigid to more rigid. Compare: Is the energy of the incident pulse equal to the energy of the reflected pulse? No, the energy of the incident pulse in this diagram is greater than the energy of the reflected pulse. Remember that *i* is proportional to *i* squared. If we observe from the diagram, *i* is approximately double. For example, if we say that the incident *i* is double the reflected *a*, then the energy of the incident wave, which is *i* (the symbol for incident energy), will be four times the energy of the reflected wave. This is because, as we learned in the previous lesson, energy depends on the rate. Here, dear student, we can study waves at boundaries with another example. This end is fixed, similar to the wave passing from a thicker spring to a thinner spring. What happens to the reflected wave here? It is reflected and inverted. If the end is fixed, what happens? It is reflected and transmitted. But what is the difference? Is there another medium that the wave travels to? No. Therefore, with the same amplitude, there might be a loss of energy due to a collision with the wall, but we can minimize this loss. So, notice here that the amplitude of the incident wave is almost the same as the amplitude of the reflected wave. We neglect the loss resulting from its collision with the wall. Therefore, we have two examples. As you can see, dear student, if the endpoint is free to move, notice here that the reflected wave is reflected in the same direction. But if the endpoint is fixed, it is reflected and inverted. So here we have two cases: if the endpoint is free to move, it is reflected only, reflected only. But here, if the endpoint is fixed, we say it is reflected and inverted. So, we have an example here. We have an endpoint free to move, we will draw it like this. We have the incident wave, we point to it with this arrow towards this wall. When it is reflected, it will be reflected in the same direction. If it is a crest, it will return as a crest. If it is a trough, it will return as a trough. If the endpoint is fixed, then if we have an incident wave, it will be reflected but inverted with approximately the same amplitude. This is regarding waves at the boundaries. Regarding wave interference, here, dear student, imagine we have two waves propagating in opposite directions. These two waves, as you can see here, dear student, have a crest and a crest. When they meet, notice that the resultant will be a larger crest. This interference is called constructive interference. What? If we have a crest and a trough, the two waves meet, and the resultant is zero after interference. The blue wave continues on its right path, and the yellow wave continues on its path. This means interference only occurs during separation. So what is interference? Interference is the meeting of two waves in opposite directions. It can be constructive interference if they are in the same direction or destructive interference if they are in opposite directions. Therefore, interference is the superposition of two waves propagating in opposite directions. Here, dear student, notice on the left: crest with crest, trough with trough. On the left, we call it constructive interference, while on the right, it is destructive interference. In constructive interference, a crest meets a crest or a trough meets a trough. In destructive interference, notice that a crest meets a crest plus a trough. In constructive interference, we add the amplitudes, so here we add the sum. Here, we subtract the amplitudes. In subtraction, the resultant is in the direction of the larger. That is, if the crest is larger, it is a crest; if the trough is larger, it is a trough; if they are equal, it is zero. Here, as you can see, dear student, we have an example: here is a crest and here is a trough. Consider the crest as... What is the bottom in terms of positive? With the negative, we will have a positive peak and a negative bottom, which will result in a positive value. So, the result will of course be a peak, and of course, this is destructive interference. Why? Because the two directions are opposite to each other here, as you can see in the diagram on the left, there is constructive interference, while in the diagram on the right there is destructive interference. Why is it constructive interference? Because when a peak meets another peak, there is a destructive overlap. Why? Because a crest meets a crest when drawing the resultant wave, notice here the amplitude. For example, let's assume it's one, and the amplitude here equals one. When the two waves meet, it will give us a larger amplitude. But here, notice here the amplitude is one, and here the amplitude is one. So when the two waves meet, the resultant is zero. We can call this interference when the resultant is zero. We call it perfect interference. When the resultant is equal to zero, it means the amplitudes are equal in magnitude but opposite in direction. Here, the student is in constructive interference. Notice here a crest meets a crest. If we denote this wave by the symbol X and this wave by the symbol Y, when they meet, it gives us a larger crest. After meeting, the Y wave continues its movement, and the X wave continues its movement. So the accumulation is only during the meeting of the two waves. The same thing happens in destructive interference. Here is a crest, and here is a trough. Of course, when they interfere, because they are equal, the resultant will almost equal zero. So this can be called perfect destructive interference. What does perfect destructive interference mean? It means the resultant equals zero after In the X-wave interference, the crest continues to the right, and the Y-wave continues to the left. Here, notice that the crest is larger than the trough. Therefore, is the resultant zero? No, it's destructive interference. We only subtract, but the resultant isn't zero. Notice that after the X-wave interference, the X-wave continues its movement, and the Y-wave continues its movement. This is constructive interference. Next, we study a type of wave: standing or stationary waves. Here, dear student, as you can see, what happens when a stationary wave, a wave propagating on a string or thread, is reflected and reversed. The crest then meets the trough of these two waves, forming a type of wave called a standing or stationary wave. It originates from the superposition of two opposing waves; that is, the crest and trough are opposite in direction. This standing or stationary incident wave consists of two parts: a node and a trough. We will denote the node by the symbol 'n' and the trough by the symbol 'i'. What do we mean by a node? Destructive interference occurs at the node, while constructive interference occurs at the trough. Building in the node, the amplitude equals zero because the two waves are equal, while in the midgut the amplitude is at its maximum. Dear student, here this point is an N node and this point is a node, while the one in the middle is a B middle. Therefore, if we draw here the number of nodes and the number of midguts, how many nodes do we have? We have two knots, but how many bellies? One belly, okay, here notice we have one knot, two, three, but the bellies are one, two, so how many knots do we have? We have three nodes and an antinode, while in the third diagram we have one, two, three, four, and the antinodes are one, two, and three. Therefore, we have four nodes and three times the length. Note that the number of nodes always equals the number of antinodes plus one. Here in this diagram, dear student, in a standing wave, each antinode represents half a wavelength. Therefore, here in the first diagram, we have one antinode, so we will have half a wavelength. In the second diagram, we have two antinodes, meaning half a wavelength, and here, half a wavelength, so we will have a full wavelength. But here, we have half a wave, and here, half a wave, and here, half a wave. Therefore, we will get one and a half waves. Let's study this diagram. We have a string vibrating between two fixed ends, as you see in the first diagram. This is called the first harmonic. Notice that it vibrates in the form of one antinode. Here, as you can see, we have a node, a node, and an antinode. If you notice, dear student, how many antinodes there are, one antinode. Therefore, the length of this string, which is the t, is equal to half a wave because it has one antinode. Therefore, the t is equal to half a wave. If we divide by half, it equals where the t is. This is what we call the t, which is the fundamental frequency. Now, this string will vibrate with this The shape is we will add a beat each time we will add a beat, so here we have one, dear student, how many knots do I have? One, where are 3? No, but how many beats? Two beats. So notice here each beat is half a beat and here each beat is half a beat. So in the second tone or the second harmonic, the length will be equal to how many beats? 1 flash, and therefore the flash is the same length. This will be double the fundamental frequency. Notice the wavelength decreases to half, the frequency increases to double. We studied this relationship because the same speed, the same clarity in the third harmonic. Notice, notice here we will add an undertone. Here we have a knot, a knot, a knot, a knot. How many undertones do we have? Three beats, each beat as we mentioned represents half a wave, half a wave, and here half a wave, and here half a wave. Therefore, we will have that L equals how many waves? 1.5, one and a half, which is how many 3/ A. Therefore, the wavelength will equal how many 2/3, so this will be 3fN. After that, we will add another beat, so we will have in this form how many knots we have. Notice one, two, three, four, five knots. As for how many beats, one, two, three, four, as we agreed, dear student, each beat represents how many half wavelengths, half a wave, here half a wave, here half a wave, here half a wave. Therefore, the length of the string here, or the length of the rope, vibrates over how many four half- waves, which is how many two waves. So the wave will be equal to half the length of the string. This is the fourth harmonic. Here, dear student, very simply, here it may give you the length and tell you to calculate the wavelength, or it may give you the wavelength and tell you to calculate the length. For example, if I told you here this is a standing or stationary wave, if this length of the rope equals 10 cm, what will the wavelength be? All you have to do is write the length of the wavelength, which is half a wavelength, so the length equals half a flash. Here, did he give us the length or the wavelength? He gave us the length, which we'll say is 10 cm. One centimeter equals half a wavelength. So, if we divide both sides by half the wavelength, it equals 20 cm. Or, conversely, he gives us the wavelength. Tell me to calculate the length of the string. So, here, for example, let's say this wave, the length is unknown, but he tells me that the wavelength, for example, equals 10 cm. What is the length of the string? All we have to do is write that the length represents how many waves. We agreed that here is half, and here is half. How much is half? Five times five, which is 2.5. So, what is 2.5 wavelengths here? And what will equal 2.5? 5 x 10, what does that equal? The length here is 25 cm. Next, we will study the waves that travel in our dimension. As you can see, dear student, the waves here are like this: if you throw a stone into water, notice that the waves spread in a circular pattern from the source. Here, we refer to the crests. The line connecting the crests of the waves is called the wavefront. The line connecting the wavefronts at the same time is the wavefront. Notice here that a ray is perpendicular to the wavefront at each point. This ray makes a right angle and indicates the direction of the wave. The wavelength here, as you know, is the distance between two values. Therefore, what is the wavelength? It is the distance between two wavefronts. Here, a flash is a flash at any two points. The distance between them, which is the distance between the crests of two wavefronts, is the wavelength because it is the distance between two waves. Here, the wave basin. Notice here the waves. The black lines are the wavefronts. The distance between two lines is called the wavelength. Every distance between two wavefronts is called the wavelength. The red arrow, which is perpendicular to the direction of wave propagation, indicates the direction of the wave. Next, we will study reflection. Notice here, dear student Before we study reflection, the first thing we'll learn is the normal. What is a normal? As you know in mathematics, a normal makes a 90- degree angle with the line. So, a normal makes a 90-degree angle with the surface. Reflection is the bouncing back of waves. Here, as you can see, are incident waves, and here is a reflected wave. Here we have an angle we'll call theta A, and here we have an angle we'll call theta R. What is theta A? It's the angle of incidence, while theta R is the angle of reflection. The angle of incidence is the angle between the incident waves and the normal. So, it's the angle between which two sides it has. What are the two sides? The incident wave and the normal. So, it's the angle between the incident wave and the normal. As for the angle of reflection, it's the angle between the reflected or bouncing wave and the normal. Notice here from the figure that the angle of incidence equals the angle of reflection. This is called the law of reflection. The law of reflection states that the angle of incidence equals the angle of reflection. It's not called what is possible. What do we write? ΔΔ, i.e., ΔΔ. Notice here, dear student, if we look at the incident waves, notice here the wavefront. Here the wavelength of the incident wave is the same as the wavelength of the reflected wave. Therefore, in reflection, notice here regarding the frequency, of course the medium has not changed, the same medium, so it will be the same speed. But here, has the wavelength changed? No, the same wavelength and therefore the same frequency. What changes, dear student? What changes is not the direction, but the direction of propagation. What changes here is the direction of the wave's propagation. Instead of the wave going to the right, it now goes down. This is what happens in reflection. As for the second phenomenon, which is wave refraction, wave refraction is also a change in the direction of wave propagation when it moves between two different media. Therefore, dear student, since I told you two different media, what will be constant? The frequency will be constant, while the speed will be constant, and the wavelength will have a direct relationship. What does the word direct relationship mean? They increase together and decrease together. The direction changes, but is it possible for the direction to remain the same? Yes, if the wave falls perpendicularly on the surface, the direction does not change. For example, if I have a surface like this and a wave falls on it perpendicularly, the wave will continue in the same direction. Notice here, dear student, if we call this first medium X and the second medium Y, notice here that the wavelength in X is greater than the wavelength in Y. Therefore, we will say that the light in X is greater than the light in Y. Of course, here are two different mediums. Depth affects the speed of the water, and therefore, what will differ with the wavelength is the speed. Therefore, the speed is directly proportional, so VX is greater than VY. But here, the speed is the same, sorry, the frequency is the same because the frequency does not change when the wave travels between two different mediums. Now, dear student, let's solve some questions. Try to evaluate yourself in solving these questions. What properties remain constant without change when a wave passes through a boundary between two different mediums? What does this mean? What process has happened ? As long as there is a boundary between two different media, if wave refraction occurs, what remains constant and what changes? What remains constant is the frequency, while what changes is the wavelength, speed, and amplitude. Amplitude can change depending on the properties of the medium, because part of the wave can propagate and part can be reflected, depending on the medium's properties. The direction also depends on the angle of incidence. If it's perpendicular, the direction won't change; if it's inclined at an angle, the direction will change. For example, in a diagram, two waves interfere, producing a wave with a larger amplitude. Since the amplitude is greater, there is interference. What kind of interference occurs? Constructive interference. Constructive interference means drawing a crest against a crest or a trough against a trough. So here we have a cataclysmic wave propagating to the right and a wave propagating to the left—two waves in opposite directions. When they interfere, there is constructive interference, and at the moment of interference, we get a larger wave. This is constructive interference. After interference, the wave that went to the left continues, and the wave that went to the right continues in its direction of motion with the same amplitude. A wave changes direction when it travels from one medium to another. Can a wave cross a boundary? Between two media without changing direction, yes, when it falls vertically, or in the probability that the wave speed is equal in both media. What is the relationship between the number of nodes and the number of antinodes in a standing wave? In a standing wave in a spring fixed at both ends, of course, dear student, as we saw in standing waves, the number of nodes increases by one, meaning the number of nodes equals the number of antinodes plus one. When a wave crosses a boundary between a thin string and a thick string, as shown in the figure, of course, this is just a figure; its wavelength and speed change, but its frequency does not. Why? What does the frequency depend on? The frequency depends on the source, which is the rate of vibration of the string, and therefore the frequency remains the same. So the frequency depends on the source. What is the source? It is the rate of vibration of the string, and therefore it remains constant. What is the difference between the pulse of a wave reflected from a fixed wall? When the wall is fixed, as we agreed, here it is an incident wave. If the end is fixed, it is reflected and inverted. So here it will be reflected and inverted. Describe the motion of particles in a medium located at a node. What do we mean by a node? This is that the amplitude of the vibration equals zero, and therefore the particles appear as if they are not moving at this point. There is no movement that crossed the front of waves at an angle from the middle of another and moved in it at a different speed. The characteristic of the two changes that occurred in the front of the waves is what changes and what remains constant, as long as we agree, is what? Frequency is what changes, as is the wavelength and direction, as shown in the diagram. The result of each case illustrated in the figure is when the center of two closely spaced pulses falls on the dotted line, causing them to completely overlap. Notice here we have a crest with a crest. If they interfere, what will we get? A larger crest? This red line represents the result of interference, and this is constructive interference. In the second diagram, notice a crest and trough of equal length. When they meet, they cancel each other out, resulting in zero. This is destructive interference, but completely destructive. What does completely destructive mean? It means the resultant is zero. Here, we have a crest and a trough, so it is destructive interference. Which is larger? The larger one is the trough, and therefore the resultant will be a trough. The red line we drew represents the resultant. The mass of the strings is the same per unit length, and they are all affected by the tension force. What does this mean? The same speed. Why? Because we said the wave speed in the medium, in the strings, or in the rope depends on... The mass per unit length and tensile strength, if it is a mass, then what are the known lengths of the strings? Wave frequencies from largest to smallest: Here, if the waves are the same length, we see that the one with more waves has a higher frequency, but here, are they the same length or different lengths? Different lengths, so we have to start counting. Of course, the basis we are working on is that each wave is half a wave, here is half a wave, here is half a wave, here is half a wave. Therefore, in the figure, what length represents how many waves? The length represents, for example, three halves, meaning one and a half waves. What is the length here ? 27 equals 1.5 waves, therefore the wavelength will be 18 cm. This is relative to what? Relative to B. Here, it's half a wave, and here, half a wave, and here, half a wave. Therefore, the length here represents how many waves: 4 x 1/2, which is two waves. The length here is 30 cm, which will equal 2 flashes. So, if the wavelength will be 15 cm, here there are also three backs, meaning one and a half. Therefore, here in CL, it equals 1.5 waves, but the length is how many centimeters? 30 cm will equal 1.5 half a wave, so the wavelength will be 20 cm. Here in D, there are four backs, 4 x 1/2, which is two. Therefore, L equals 2 flashes, and so the length here is how many centimeters? 24 cm will equal 2 flashes, so the wavelength will be 12 cm. Therefore, if we arrange them according to wavelength, which has the longest wavelength? The longest wavelength is 20 cm, which is the flash. C is greater than the flash, meaning greater than the flash. B is greater than What does this pulse mean? It means frequency. It's based on frequency. The frequency is reversed, meaning reversed. FD is greater than PF, which is greater than EF, which is greater than EF. What about speed? The same speed. Why? The same mass of the strings per unit length and the same tension force. Illustrate the result of each of the three cases shown in the figure. When focused, the center of the two closely spaced pulses lies on the dotted line between them. Here, dear student, to understand this diagram, draw two pulses. Here, the left pulse arrives like this, and the right pulse arrives exactly on it. So, if we draw them, we will draw them exactly on it. Notice that each point supports the other, so the resultant here will be a larger peak. In this second diagram, if we observe the pulse on the left, it arrives like this. And the pulse on the right arrives like this. Here, dear student, so you don't get confused, if we look at this point, here the displacement is zero, and here the displacement is a shear value, so it will be a maximum value. Here the displacement is zero, and here it is a maximum value, so it will be the total. Here, the total value is a maximum value. What about the middle? At the point in the middle, this is half and this is half, so it will also be a maximum value. Therefore, the resultant will be like this. So, when these two pulses meet, the resultant will be like this. We have these two waves. The left pulse will be like this and the right pulse will be like this. I am just drawing the two pulses here. Dear student, take some points. Here, the displacement is zero. Here, the displacement is a maximum value in the negative. Therefore, the resultant will be a maximum value in the negative. Okay, at the point above, here is zero and here is a maximum value in the positive. So, what will the resultant be a maximum value in? With the positive, notice here is a positive value and here is a negative value, so the resultant will be zero. Therefore, dear student, I have three points above, here is zero, here is the maximum negative value. We will connect these two points together, so it will be like this. As for the wave in Figure 4, the left wave will be like this and the right wave will be like this. Notice that they are exactly the same shape, but one is positive and one is negative. Therefore, when they meet, what will the resultant be between them? Zero. This red line, which is the shape of the two waves when they meet, represents a stationary wave. A stationary wave is symmetrical, so this is wrong and this is wrong. The two waves are in opposite directions, so this is wrong. So this is correct: A stationary wave is created from the superposition of two symmetrical, opposite waves that propagate in the same medium. What is the name of the phenomenon that describes the behavior of a wave in which the direction of the wave changes? When? When it moves from one medium to another, it's called refraction. But when it moves within the same medium, it's called reflection. The mass of all the strings is the same per unit length, and they are all affected by the tension force. This means we would say the same speed if the lengths of the strings are known. Arrange the waves according to wavelength from largest to smallest. The next question is the same, but arrange them according to frequency. Here's what the student would think: if you notice the same wavelengths, then if we arrange them according to frequency, which has the most waves? FE, then FC, then PF, then DF. Why? Because the length is the same, therefore the greater number of waves is a, and the wavelength will be the opposite, meaning here a, i.e., a, d, is the light, this will be greater, then they pass c, so here this is the correct answer, but on the condition that what we did here is a greater than c, because here they have the same length. Now, if they are different in length, rely on the relationship we made. What did we say here? What will be equal to how many waves? How many times? 1 2 3 4 5 6 7 8 9 9 × half of 4.5. So what will be equal to here? 4.5 is the wavelength, but how much is it here? 27 times 27 equals 4.5 waves, so how many centimeters will one wave be? Here, count with me: 1, 2, 3, 4, 5 multiplied by half equals 2.5, which is half a wave. So here, what will equal 2.y is a wave. What is here again? 27, so 27 will equal 2.y waves. One wave will be approximately 10.8 cm. Count with me: 1 2 3 4 5 6. One-half equals three waves. Therefore, the wave here will equal 3 waves. 27 will equal 3 waves. So, if one wave will equal 9 cm, then 1 2 3 × one-half, which is 1.5 flashes. Therefore, the wave representing 1.y of 27 will equal 1.5 waves. So, one wave will equal 18 cm. Here, we want to determine the longest wavelength according to the wavelength. Notice here: 6, here 10.8, 8 seconds, here 18, here t. The longest is D, followed by B, then C, then A. The same result we obtained regarding frequency, in reverse: A, then C, then B, then D. Frequency is the opposite of wavelength. When the speed is constant, two wave pulses move on the same string towards each other. Notice here the crest and here A trough remains, resulting in destructive interference. The interference is destructive in the greater direction, so the resultant will be a trough. A wave pulse reaches a fixed end, so the end here remains fixed. Consequently, the reflected wave will be inverted, meaning it will have the same amplitude. Here, no wave has passed to the other end; it has been reflected. There might be a slight energy loss due to its collision with this wall, but we neglect this loss, so we say it is inverted and has the same amplitude. When wave pulses meet and superpose, the maximum displacement of the medium is reached. Note here: crest with crest, meaning there will be interference as long as they are in the same medium, crest with crest or trough with trough. We add here: 3 here and 3 there, so 3 equals 6 cm. Two wave pulses move on the string in the same direction as each other, as shown in the example of wave interference. Here, dear student, draw the two pulses when they meet. Here is the first pulse and here is the second pulse. Note here, dear student, that this part is the same as this part, but only one. One positive and the other negative, so they cancel each other out. The resultant that will remain with us is the triangle. Here, subtraction of destructive interference. Which of the following statements is correct regarding the relationship between the wavefront and the rays? Of course, we agreed that they are perpendicular. The ray is always perpendicular to the wavefront. During play, two children form a stationary wave in a rope, or a stable wave, or a standing wave, as shown in the diagram below. A third child participates by jumping over the rope. What is the wavelength of this rope? Of course, here, one wavelength means how many waves? That means half a wave, so the length here represents half a wave. What length did he give us? 4.30 equals half a wavelength. If we divide by half the wavelength, we get 8.60, which is 60 meters. What does this shape represent? Refraction. Since we have two different media, it's called refraction. So explain why the wave changes direction. We'll say it's because of the wave's refraction as it travels. The most important thing is that it changes direction when it travels at an angle between two media with different speeds. Here, dear student, if we look at the diagram, notice that the wavelength of A is greater than the wavelength of B. So here, A is greater than B, and therefore, F is greater than F. But notice that the same frequency in the medium where the speed is greater and the wavelength is greater is deeper, while the other medium is shallower. So here, dear student, which of the two regions, A or B, is shallower? Of course, the shallower one will be A. Why me? Lower speed and shorter wavelength. What will happen to all of these quantities when the wave travels from a to b? As we observed, the speed decreases, the wavelength decreases, and the frequency remains constant. As long as it falls non-perpendicularly, the direction will change. And with that, we have finished this lesson. Thank you, and I wish you success. Peace, mercy, and blessings of God be upon you. Yeah.