Grasping Superposition Concept: Physics 122 (Algebra Based)

In summary: This can be visualized as the points on the waves overlapping and combining to create a new, net displacement. This concept is described in detail in College Physics by Knight, Jones, and Field, in the 1e edition on page 515, figure 16.3.
  • #1
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I am having a hard time grasping this concept. More specifically, I am having a hard time finding the net displacement of two waves when they are overlapping. My book describes the net displacement of two waves as the point-by-point summation of the individual waves.

the bold statement is where I am getting lost. I know summation is just the sum of all the points. But are they talking about points on the Wave? Points on the graph?

I'm in physics 122(algebra based) the second half of physics. My teacher is using College Physics by Knight, Jones, Field. If anyone has the same book the diagram is on pg 515 Figure 16.3.

Thanks!

Edit: It is the 1e which is the only edition of that book...
 
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  • #2
The net displacement of two waves is the sum of the individual displacements at each point in space and time. For example, if you have two sine waves with amplitudes A1 and A2 and wavelengths λ1 and λ2, their net displacement at a given point in space and time would be A1*sin(2π*x/λ1) + A2*sin(2π*x/λ2), where x is the position along the direction of propagation. In other words, you add up the individual displacements of the two waves at each point in space and time.
 
  • #3


Hello there,

I understand that you are struggling with grasping the concept of superposition in your physics class. Superposition is a fundamental principle in physics that states that when two or more waves overlap, the resulting wave is the sum of the individual waves at each point. This means that at any given point, the displacement of the resulting wave is equal to the sum of the displacements of the individual waves at that point.

To better understand this concept, it may be helpful to think of the waves as a series of points on a graph. Each point on the graph represents the displacement of the wave at that particular point in time. When two waves overlap, the resulting wave is the sum of the displacements of the individual waves at each point. This can be visualized by adding the values of the individual waves at each point on the graph.

In your book, the net displacement of two waves is described as the point-by-point summation of the individual waves. This means that you need to add the displacements of the individual waves at each point to find the net displacement of the resulting wave. This can be done by adding the values of the individual waves at each point on the graph.

I would recommend practicing with different examples and diagrams to help you better understand this concept. You can also try discussing it with your teacher or classmates for further clarification. Keep in mind that understanding superposition is crucial in many areas of physics, so it is important to spend some time on it and ask for help when needed.

I hope this helps and good luck with your studies!
 

Related to Grasping Superposition Concept: Physics 122 (Algebra Based)

1. What is superposition in physics?

Superposition in physics refers to the principle that when two or more waveforms meet, the resulting waveform is the sum of the individual waveforms. In other words, the amplitude of the combined waveform is equal to the sum of the amplitudes of the individual waveforms. This principle is fundamental to understanding the behavior of waves, such as light and sound, and is also applicable to other physical phenomena, such as quantum mechanics.

2. How does superposition relate to algebra in physics?

In algebra-based physics, superposition is used to simplify the analysis of complex systems by breaking them down into smaller, simpler components. By understanding the individual components and their effects on the overall system, we can use algebraic equations to calculate the resulting waveforms or other physical quantities.

3. Can you give an example of superposition in action?

One example of superposition is the interference pattern created by two overlapping waves. When two waves with the same frequency and amplitude meet, they will create an interference pattern with alternating regions of constructive and destructive interference. This can be seen in the classic double-slit experiment, where a single beam of light is split into two and then recombined to create an interference pattern on a screen.

4. What are the limitations of superposition in physics?

While superposition is a useful concept in physics, it does have its limitations. It is based on the assumption that the individual components do not interact with each other, which is not always the case in real-world situations. Additionally, superposition can only be applied to linear systems, meaning that the resulting waveform is directly proportional to the individual components. Non-linear systems, on the other hand, can exhibit more complex behaviors that cannot be described by superposition.

5. How is superposition used in quantum mechanics?

In quantum mechanics, superposition is a key concept that explains the wave-like behavior of particles on a microscopic scale. According to the principle of superposition, a quantum particle can exist in multiple states simultaneously until it is observed or measured, at which point it "collapses" into a single state. This idea is fundamental to understanding phenomena such as quantum entanglement and the double-slit experiment.

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