Main source: http://www.mathpages.com/home/kmath242/kmath242.htm

On this article, as far as I understand, the author claims that wave behavior on even dimensions would give rise to many waves with infinitely different velocities, all spreading outwards. In the context of even dimensions, it wouldn’t spread cleanly, but diffusely.

See quote: “For the case of two dimensional space this doesn't work (...) We can still solve the wave equation, but the solution is not just a simple spherical wave propagating with unit velocity. Instead, we find that there are effectively infinitely many velocities, in the sense that a single pulse disturbance at the origin will propagate outward on infinitely many "light cones" (and sub-cones) with speeds ranging from the maximum down to zero.”

However, I was informed by another source (a fellow forum user here) that the best way to describe wave behavior on even dimensions is that it, while going forward, also keeps reflecting back, generating backward waves. Now, which is the right interpretation of the refered article? Because as long as I understand there’s no mention of backward wave canceling only on odd dimensions and not on even dimensions (only that it doesn’t propagate sharply on the latter).

The refered dialogue with fellow user can be found here on comments: Open-open pipe standing waves

  • 1
    $\begingroup$ Actually both quotes are just different ways of phrasing the same thing, though I have a minor quibble with the second one. $\endgroup$
    – knzhou
    Aug 8, 2018 at 19:54
  • $\begingroup$ As I see, one point source emanating “a series of waves” of multiple velocities, all outwards, is an altogether different thing than waves going forward and backwards at the same time, hence my confusion with the colleague’s interpretation $\endgroup$
    – user137288
    Aug 8, 2018 at 20:04
  • $\begingroup$ I’d be very pleased if you could elaborate more on your interpretations, but thanks in advance $\endgroup$
    – user137288
    Aug 8, 2018 at 20:06
  • 1
    $\begingroup$ Sorry, I was getting to it but have been busy! I'll type up a long-ish answer by the end of the weekend. $\endgroup$
    – knzhou
    Aug 9, 2018 at 20:44
  • 1
    $\begingroup$ researchgate.net/publication/340085346 $\endgroup$
    – user45664
    Mar 22, 2020 at 18:18


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