Exploring 4D Wave Propagation in 3D Solids

In summary: I am not sure what you are asking, but you can study the wave equations in any number of space dimension. You can find a lot of literature on subject, just do a web search.
  • #1
ScientificMind
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Is there any research on "waves" in a three dimensional solid caused by said solid propagating through a fourth dimension?
I am uncertain if this belongs in the differential geometry thread because I don't know what area of mathematics my question belongs into begin with, but of the math threads on physics forums, this one seems like the most likely to be relevant.
I recently watched a video by PBS infinite series called "Can We Hear Shapes?" about waves propagating through 2 dimensional surfaces, linked here:
This got me wondering though. Waves propagate through a 1D line by making the line oscillate through a second dimension and a wave propagates through a 2D surface by making said surface oscillate through a third dimension. There is no real-world analogue to 3D solids, but it should be possible to at least model or abstractly analyze waves propagating through a 3D solid by making it oscillate through a fourth dimension.
What I want to know is if anyone has done any research on this before. Is there anywhere I can go to read about this sort of thing? Or, if there hasn't been any actual research on it, has the topic ever at least been mentioned in passing in a mathematical context?
 
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  • #2
Not sure what you are asking, but you can study the wave equations in any number of space dimension. You can find a lot of literature on subject, just do a web search.
 
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  • #3
Hey i might understand what you are trying to say .. i am also looking for same kind of study ... did you found anything about it. can you send me some link of books or any research about this.
 
  • #4
Im looking for a book myself on the subject of Differential Geometry but I may just dive through the forumns for awhile.
 
  • #5
AbyssalPloy said:
Im looking for a book myself on the subject of Differential Geometry but I may just dive through the forumns for awhile.
Welcome to PF. :smile:

Go ahead and start a new thread in the Science & Math Textbooks forum (in the Education section of PF), and give as much information as you can about what you are looking for. You should get good suggestions. Also, once you've created your new thread, take a look at the bottom of the thread to see what "Related Threads" the forum software finds that have similar thread titles.
 
  • #6
ScientificMind said:
Summary: Is there any research on "waves" in a three dimensional solid caused by said solid propagating through a fourth dimension?

I am uncertain if this belongs in the differential geometry thread because I don't know what area of mathematics my question belongs into begin with, but of the math threads on physics forums, this one seems like the most likely to be relevant.
I recently watched a video by PBS infinite series called "Can We Hear Shapes?" about waves propagating through 2 dimensional surfaces, linked here:
This got me wondering though. Waves propagate through a 1D line by making the line oscillate through a second dimension and a wave propagates through a 2D surface by making said surface oscillate through a third dimension. There is no real-world analogue to 3D solids, but it should be possible to at least model or abstractly analyze waves propagating through a 3D solid by making it oscillate through a fourth dimension.
What I want to know is if anyone has done any research on this before. Is there anywhere I can go to read about this sort of thing? Or, if there hasn't been any actual research on it, has the topic ever at least been mentioned in passing in a mathematical context?

miss PBS Infinite Series lol
 

1. What is 4D wave propagation?

4D wave propagation refers to the study of how waves travel and interact in four-dimensional space, which includes three dimensions of space and one dimension of time. It is a complex phenomenon that is still being studied and understood by scientists.

2. How is 4D wave propagation different from 3D wave propagation?

4D wave propagation is different from 3D wave propagation because it takes into account the element of time. In 3D wave propagation, the waves are studied in three dimensions of space, but in 4D, the waves are also analyzed in relation to time, which adds an extra dimension to the study.

3. Why is it important to explore 4D wave propagation in 3D solids?

Exploring 4D wave propagation in 3D solids is important because it can help us better understand and predict the behavior of waves in real-world scenarios. This knowledge can have practical applications in fields such as engineering, seismology, and materials science.

4. What techniques are used to study 4D wave propagation in 3D solids?

Scientists use a variety of techniques to study 4D wave propagation in 3D solids, including computer simulations, mathematical models, and laboratory experiments. These methods allow them to observe and analyze the behavior of waves in different materials and conditions.

5. What are some potential future developments in the study of 4D wave propagation in 3D solids?

As technology and scientific understanding continue to advance, there are many potential future developments in the study of 4D wave propagation in 3D solids. These may include more accurate and detailed simulations, the development of new materials with unique wave propagation properties, and the application of this knowledge in various industries and fields.

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