- #1

- 48

- 1

## 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?

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?