Waves in 4D

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 in to 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?

Answers and Replies

martinbn
Science Advisor
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.

LCSphysicist and ScientificMind
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.

Im looking for a book myself on the subject of Differential Geometry but I may just dive through the forumns for awhile.

berkeman
Mentor
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.

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.

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 in to 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