unit 8 SUPERPOSITION

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[Audio] When two or more waves meet at a point, the resultant displacement at that point is equal to the sum of the displacements of the individual waves at that point. This principle, known as superposition, can be observed in various experiments, such as those involving microwaves, stretched strings, and air columns, where stationary waves are formed. In these experiments, it is assumed that end corrections are negligible, and knowledge of this concept is not required. Furthermore, by using a graphical method, one can understand the formation of a stationary wave and identify its nodes and antinodes. Additionally, the positions of these nodes and antinodes can be used to determine the wavelength of the stationary wave. This concept is essential in the study of waves and their behavior..

[Audio] In this section, we will discuss interference and coherence. Candidates should be able to understand these terms and have a solid understanding of experiments that demonstrate two-source interference. These experiments can be carried out using various mediums such as water waves in a ripple tank, sound, light, and microwaves. It is important for candidates to also understand the conditions required for two-source interference fringes to be observed. They should be able to recall and use the equation ax/D for double-slit interference using light. Furthermore, in section 8.4, we will focus on the diffraction grating. Candidates should be able to recall and use the equation d sin θ = nλ and describe the use of a diffraction grating to determine the wavelength of light. The structure and use of a spectrometer will not be included in this discussion..

[Audio] When two or more waves meet or overlap, they form a resultant wave. The displacement at any point is the sum of the displacements of the individual waves. This phenomenon is known as interference. It's not limited to specific types of waves - we can observe interference with all kinds of waves..

[Audio] When two or more waves meet at a point, their combined effect is the sum of their individual effects. This fundamental principle is known as superposition. Imagine two waves, one with a crest and another with a trough, meeting at a single point. The resulting wave would have a displacement equal to the sum of the displacements of the individual waves. This concept is crucial in understanding various phenomena in physics, such as sound and light waves..

[Audio] When two waves of the same frequency arrive at a point in phase, they interfere in such a way that the resultant wave has a higher amplitude. This phenomenon is known as constructive interference..

[Audio] When adding two waves by the principle of superposition, the resulting wave is represented by the red line. The distance between the two waves determines the phase relationship between them, which in turn affects the resulting wave when they are added together. A change in distance can result in a change in phase, leading to a different outcome when the waves are combined. The shape and amplitude of the resulting wave are directly influenced by the distance between the initial waves. Understanding the concept of distance in superposition is key to accurately predicting the resulting wave and analyzing and manipulating waves to achieve the desired outcome..

[Audio] When two waves of the same frequency arrive at a point in phase, they interfere constructively, resulting in a larger amplitude. On the other hand, if the waves are out of phase, they interfere destructively, resulting in a weaker amplitude. The same principles apply when more than two waves interact with each other, with the resulting interference being determined by the combined effects of all the overlapping waves..

[Audio] When two waves meet at a point, they combine according to the principle of superposition. The phase difference and the path difference between the two waves are crucial factors to consider. The phase difference refers to the difference in the phase angle of the two waves, while the path difference represents the difference in the distance travelled by the two waves. By combining these two factors, we can better comprehend how the waves interact with each other..

[Audio] When two waves meet at a point, their combined effect depends on the path difference between them. This path difference is the extra distance one wave travels compared to the other. Whether the waves add together constructively or cancel each other out destructively depends entirely on this path difference..

[Audio] When the waves from the red source have travelled three whole wavelengths and the waves from the yellow source have travelled four whole wavelengths, we find that the path difference between them is one wavelength. Since this path difference is equal to a phase difference of zero, it means that these waves are in phase with each other. As a result, they interfere constructively, producing a resultant wave with double the amplitude. Now, let's consider what would happen if the situation were different..

[Audio] When the waves from the red source and the yellow source combine, they interfere destructively because they are in antiphase. This means that the peaks of one wave align with the troughs of the other, resulting in a cancellation of the amplitudes..

[Audio] The curve we see here represents the relationship between two variables. As one variable increases, the other variable also changes, following this curved path. The shape of the curve can tell us about the strength and direction of their connection..

[Audio] The grid we see here represents the underlying structure of our physical world. It's a fundamental concept in physics, where we can observe how different waves interact with each other. Superposition is the ability of two or more waves to coexist and combine their effects. In this image, we're looking at a close-up of a grid, which shows us how these waves overlap and create new patterns. This is a crucial aspect of physics, as it helps us understand many phenomena in nature..

[Audio] Class ACTIVITY #6 Questions 1-3 Page 161 Questions 5-6 Page 162-163 Question 12 Page 165-166 Slide 28 Diffraction Grating What is a diffraction grating? A device made of many parallel slits or lines, used to diffract light. How does it work? Light passes through the slits or lines and creates an interference pattern on a screen. Slide 29 Diffraction Grating What is the equation for the diffraction grating? d sin θ = nλ Where: * d is the distance between the slits or lines * θ is the angle of diffraction * n is an integer * λ is the wavelength of light Slide 30 Diffraction Grating What is the purpose of the diffraction grating? To determine the wavelength of light Slide 31 Diffraction Grating What is the advantage of using a diffraction grating over a single slit? The diffraction grating produces a more intense and sharper spectrum than a single slit. Slide 32 Diffraction Grating What is the disadvantage of using a diffraction grating? It requires precise alignment and careful handling to avoid damage. Slide 33 Diffraction Grating What is the application of the diffraction grating? In spectroscopy, to analyze the composition of materials by identifying their characteristic spectra. Slide 34 Diffraction Grating What is the limitation of the diffraction grating? It can only measure the wavelength of light within its range of resolution. Slide 35 Diffraction Grating What is the future development of the diffraction grating? Advancements in technology will lead to improved precision and wider range of applications. Slide 36 Diffraction Grating Typical Conditions for Interference Patterns on page 139 (Table 8.1) Class ACTIVITY #7 Questions 1-3 Page 167 Questions 5-6 Page 168-169 Question 12 Page 172-173 Slide 37 Diffraction Grating What is the conclusion of the diffraction grating? The diffraction grating is a powerful tool for analyzing the properties of light and its applications in various fields. Slide 38 Diffraction Grating What is the recommendation for further study? Further study of the diffraction grating and its applications will provide a deeper understanding of the principles of physics and its relevance to real-world problems. Slide 39 Diffraction Grating What is the final thought? The diffraction grating is a fundamental concept in physics that has far-reaching implications and applications in various fields, making it an essential topic for students to learn and understand. Slide 40 Diffraction Grating What is the last slide? Typical Conditions for Interference Patterns on page 139 (Table 8.1) Class ACTIVITY #8 Questions 1-3 Page 174 Questions 5-6 Page 175-176 Question 12 Page 179-180 Slide 41 Diffraction Grating What is the next step? Continue learning and exploring the concepts of diffraction gratings and their applications in various fields. Slide 42 Diffraction Grating What is the final message? Remember, the diffraction grating is a powerful tool for analyzing the properties of light and its applications in various fields. Keep learning and exploring!.

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CLASS ACTIVITY #3. Page 129 Question 11c.

[Audio] The signal generator produces a 500 Hz sine wave. This wave can be thought of as a single-frequency component of a more complex waveform. In the context of superposition, this means that we have a single-frequency component added to other components, resulting in a more complex waveform. We can think of this process as adding the 500 Hz sine wave to other frequencies, allowing us to create a new waveform with multiple frequency components. This is the fundamental principle of superposition, where the addition of multiple waves results in a new wave with unique properties..

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[Audio] Coherent waves are waves that maintain a constant phase difference. They can be described as waves that are "in sync" with each other. This means that the peaks and troughs of the waves line up, resulting in a strong and consistent wave pattern. One example of coherent waves is a laser beam. The light waves produced by a laser are coherent, meaning they are all in phase with each other. This allows for a concentrated and powerful beam of light. Coherent waves are also important in many everyday applications, such as in communication systems and medical imaging. By understanding the properties of coherent waves, we are able to harness their power and utilize them in various technological advancements. Coherent waves can help us better understand the behavior of light and other electromagnetic waves. Through studying coherent waves, we are able to gain a deeper understanding of wave mechanics and how they interact with each other. Coherent waves are waves that maintain a constant phase difference and play a vital role in various fields, from technology to science..

[Audio] The path difference between points A and B is equal to the distance between the slits multiplied by the order of the bright fringe, which is n times lambda..

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[Audio] When two or more waves overlap in space and time, their resulting amplitude is the sum of their individual amplitudes according to the principle of superposition. This means that the resulting wave has the same frequency as the original waves, but its amplitude can vary depending on the phase difference between the waves. In other words, the resulting wave is the algebraic sum of the individual waves. This principle is crucial in understanding various physical phenomena, such as the behavior of sound and light waves..

[Audio] Diffraction is defined as the spreading of a wave into regions where it would not be seen if it moved only in straight lines after passing through a narrow slit or past an edge..

[Audio] Answer: When waves pass a single slit, they do not produce an interference pattern. Instead, the wavefront is diffracted around the edges of the slit, creating a diffraction pattern. This is because the single slit acts as a point source, producing a spherical wavefront that spreads out in all directions. As a result, the wavefront is no longer coherent, and the interference pattern is lost. We can only observe an interference pattern when there are multiple sources or paths for the waves to follow, such as in a double-slit experiment..

[Audio] The path difference between points B and A is half the distance between them, which is half a time theta. Since this is equal to half a wavelength, we can set it equal to half lambda. Then, we substitute theta for sine theta and solve for lambda. This yields the equation lambda equals 2a divided by n, where n is the order of the dark fringe..

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1 2 3 4 5 path difference = d sin 9 d = slit spacing light diffracted at eto normal.

DIFFRACTION.

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[Audio] Two waves with different frequencies and amplitudes are added together using the principle of superposition. The time array is generated using the numpy library, and the phases and displacements of the two waves are calculated. The resultant displacement is then plotted using the matplotlib library, showing the combined effects of the two waves..

[Audio] Typical conditions for interference patterns include the presence of two coherent sources, a flat surface, and a suitable distance between the sources and the surface. When these conditions are met, we can observe the formation of interference patterns such as bright and dark regions. These patterns arise due to the superposition of the waves emitted by the two sources. The table on page 139 provides a comprehensive list of typical conditions for interference patterns, which can be used to analyze and understand various phenomena in physics..

[Audio] Vibrations are a type of wave motion where the particles of the medium oscillate about their mean position. Stationary waves, on the other hand, are a type of wave motion where the particles of the medium do not move along their mean position. Instead, they oscillate with a fixed phase relationship. The main difference is that vibrations involve movement of particles along their mean position, whereas stationary waves involve no net movement of particles..

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[Audio] The pulse is travelling in an outward direction. There are three different types of pulses: the outward pulse, the reflected pulse, and the fixed pulse. The outward pulse is currently travelling along the slinky, the reflected pulse bounces back when it reaches the end of the slinky, and the fixed pulse remains in place. The fixed pulse is not affected by the movement and remains in place. The fixed end of the slinky plays a key role in preventing the waves from interfering with each other. Superposition is a complex phenomenon that can be observed in many different systems..

[Audio] When we have a stationary wave pattern, nodes are points where the displacement is zero, and antinodes are points where the displacement reaches its maximum value. Nodes do not move as the wave passes through them, while antinodes move with the maximum amplitude. The distance between two adjacent nodes or antinodes is equal to half the wavelength, and the distance between an antinode and a node is equal to one quarter of the wavelength..

[Audio] In this slide, we discuss the concepts of amplitude, displacement, resultant, and distance related to waves. Amplitude denotes the maximum height of a wave, while displacement signifies the distance from the equilibrium point to the crest or trough of a wave. The resultant represents the combination of two or more waves, and distance refers to the length of a wave. On the slide, we see the letters "s" and "x", representing the wave moving to the right and left respectively. Furthermore, we observe the separation between two adjacent nodes or between two adjacent antinodes, which equals half the wavelength. The separation between an adjacent node and antinode is equal to one-quarter of the wavelength. These values are crucial in comprehending the properties of waves. We proceed to the next slide, where we examine the phenomenon of interference and its impact on wave behavior..

[Audio] The wavelength of the stationary wave can be calculated by considering the separation between adjacent nodes. Since the nodes are separated by 25 cm, we can calculate the wavelength as follows: Wavelength = 2 x Separation between nodes = 2 x 0.25 m = 0.5 m. So, the wavelength of the stationary wave is 0.5 m. As for part b, the distance from a node to an adjacent antinode is half the wavelength. Therefore, Distance from node to antinode = (0.5 m)/2 = 0.25 m..

[Audio] Transverse standing waves are formed when the frequency of the wave matches the length of the string, causing the waves created from one end of the string to bounce off the other end and reinforce each other, resulting in a stationary wave pattern. The lowest frequency standing wave pattern is the fundamental mode, and increasing the frequency creates higher harmonics or overtones, each with its own unique characteristics, such as nodes and antinodes..

[Audio] When we have a stationary wave, we can observe that there are points where the displacement is zero, known as nodes. Additionally, there are points where the displacement is maximum, referred to as antinodes. Furthermore, we can notice that the distance between consecutive nodes or antinodes is equal to half the wavelength, denoted by λ. Therefore, if we measure the distance between two nodes or antinodes, we can determine the wavelength..

[Audio] In a stationary wave pattern on a string, the amplitude of vibration varies with position along the string. At nodes, the amplitude is zero, while at antinodes, it reaches its maximum value. Unlike progressive waves, where the crests and troughs move along the string, the nodes and antinodes remain fixed. Furthermore, between adjacent nodes, all points of the stationary wave vibrate in phase, whereas in a progressive wave, phase varies continuously along the wave. Additionally, there are only specific frequencies of stationary waves possible on the string, which depend on the length of the string and the speed of the progressive waves that form the stationary wave..

[Audio] The air molecules vibrating with maximum amplitude is an antinode, where the air molecules do not vibrate at all is a node..

[Audio] The air molecules here are vibrating with maximum amplitude, indicating an antinode. At this point, there is no vibration of the air molecules, signifying a node. The diagram illustrates the fundamental, second, and third modes of vibration of air in a closed pipe, corresponding to distinct frequencies and wavelengths of the stationary waves formed within the pipe..

Class ACTIVITY #9. Question 18 Page 157.

[Audio] As we conclude our discussion, let's examine the concept of stationary waves. Stationary waves arise from the superposition of two progressive waves of equal amplitude and frequency, moving in opposite directions. When these waves intersect, they form a pattern comprising nodes and antinodes. Nodes signify points of zero displacement, whereas antinodes denote points of maximum displacement. The distance between consecutive nodes is referred to as the wavelength of the stationary wave. The frequency of the wave is determined by the frequency of the progressive waves that generated it. Furthermore, the speed of the wave equals the speed of the progressive waves. By grasping the characteristics of stationary waves, we can better comprehend the behavior of sound and light waves. Additionally, we can leverage them in various technologies, such as musical instruments and communication devices..