= Regular time-harmonic spherical wave
{title2=$u(r,t)=A\sin(\omega t)\,\sin(\omega r/c)/(\omega r/c)$}
For a <spherically symmetric function>, $v=ru$ reduces the radial <wave equation> to $v_{tt}=c^2v_{rr}$. A time-harmonic separated solution has radial numerator $C\sin(kr)+D\cos(kr)$, with $k=\omega/c$. Finiteness at the origin excludes $D$, and the prescribed finite origin value fixes $C$. This is a standing combination of incoming and outgoing waves. A purely outgoing point-source wave instead has a $1/r$ singularity and must be specified by its source strength, not by a finite value at the origin.
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