Does the N-Dimensional Wave Equation Apply Beyond 1-2 Dimensions?

AI Thread Summary
The discussion centers on the scaling of the standard homogeneous wave equation beyond typical 1-2 dimensional cases. It highlights the n-dimensional wave equation, which is expressed as ∂²U/∂t² = c²∇²U. Participants mention potential applications, particularly in the context of spherical waves and spherical harmonics. The conversation suggests that while there are known applications, further exploration of n-dimensional scenarios could reveal additional uses. Overall, the topic emphasizes the relevance of higher-dimensional wave equations in various fields.
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I Looked around the web for a while and had not found anything so I figured I'd ask you all about this. It's been awhile since I took a PDE course, but given your standard homogeneous /\u = 0 wave equation, does it scale above and beyond the typical 1-2 dimensional cases? If so, what are some common applications?
 
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The n dimensional wave equation is given by

\frac{\partial^2 U}{\partial t^2} = c^2\nabla^2U

Common applications? I assume there are many applications for spherical waves / spherical harmonics, but that's all I can think of.
 
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