In the book "when Einstein walked with Gödel" the author talks about Edwin A. Abotts "Flatland" stating that one problem which was unattended by Abott is the problem of acoustics in a world with an even number (in this case 2) of dimensions. He says that in spaces with an even number of dimensions a gunshot (or any "disturbance") will generate a system of waves that will reverberate forever. Can someone explain to me why that is?
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1Related: Why is Huygens' principle only valid in an odd number of spatial dimensions? – Qmechanic Dec 06 '23 at 11:38
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From what I read in the linked post, in an odd number of dimensions you can predict the wavefront at a plane by adding up waves from each point in the source as they arrive. But in an even number of dimensions, you may also need to add up waves that have already passed through the plane. But it isn't clear to me at all why this is. – mmesser314 Dec 06 '23 at 15:45
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Related Math SE Question: "Waves in spaces of even dimension". – David Bailey Dec 13 '23 at 06:29
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Thank you! I admit that I dont understand the math behind it but at least now I know what I was trying to understand. – Juliane Dec 14 '23 at 14:44