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Jun 9, 2017 at 19:57 comment added nasu There is no "R" in the original article. The position is determined by the variable "r" both in the amplitude and in the phase terms. The amplitude simply decreases as 1/r and does not depend on time. There is no angular dependence as the source emits equally in all directions (see text of article).
May 18, 2015 at 6:05 comment added Victor Pira Well, it makes sense, because $p(r,\theta,0) = 0$ everywhere except $r=0$ (if you assume a point source located at the origin). That's actually given by initial conditions - you need to state what's going on in $t,r = 0$. The equation then shows a development since then. Nice discussion of these phenomena is in the first parts of Howe's theory of vortex sound
May 18, 2015 at 4:56 comment added Amzocks Thanks a lot ! Indeed it should be rather simple but what you say implies that at $t=0, p(r,\theta,0) > 0$. Which makes me wonder about the causality of the wave propagation. Isn't it weird ?
May 17, 2015 at 17:52 history answered Victor Pira CC BY-SA 3.0