Editing Wave equation (section)

====Monochromatic spherical wave====
[[File:Spherical Wave.gif|thumb|Cut-away of spherical wavefronts, with a wavelength of 10 units, propagating from a point source]]
Although the word "monochromatic" is not exactly accurate, since it refers to light or [[electromagnetic radiation]] with well-defined frequency, the spirit is to discover the eigenmode of the wave equation in three dimensions. Following the derivation in the previous section on [[#Plane-wave eigenmodes|plane-wave eigenmodes]], if we again restrict our solutions to spherical waves that oscillate in time with well-defined ''constant'' angular frequency {{mvar|ω}}, then the transformed function {{math|''ru''(''r'', ''t'')}} has simply plane-wave solutions:<math display="block">r u(r, t) = Ae^{i(\omega t \pm kr)},</math>
or
<math display="block">u(r, t) = \frac{A}{r} e^{i(\omega t \pm kr)}.</math>

From this we can observe that the peak intensity of the spherical-wave oscillation, characterized as the squared wave amplitude
<math display="block">I = |u(r, t)|^2 = \frac{|A|^2}{r^2},</math>
drops at the rate proportional to {{math|1/''r''<sup>2</sup>}}, an example of the [[inverse-square law]].