Animation 3
The uniform plane wave is a 1-D wave in rectangular coordinates. For example, for propagation along z, it satisfies
.
This comes from the general 3-D wave equation
,
and the fact that the plane wave is constant along the other two coordinates, i.e.,

There are 1-D waves in cylindrical and spherical coordinates, too. They, however, look quite different from the plane wave. The plane wave has a flat front, while the 1-D wave in cylindrical coordinates has a cylindrical front, and the 1-D wave in spherical coordinates has a spherical front.
The common feature is that in all these coordinate systems the 1-D waves are constant with respect to two of the coordinates. For example, in cylindrical coordinates, the 1-D wave depends only on ρ , while in spherical coordinates—only on r.
Thus, the 1-D wave equation in cylindrical coordinates is
.
Observe an outgoing (Gaussian pulse) cylindrical wave (the analog of the incident plane wave). It propagates along the + ρ axis.

Observe an incoming cylindrical wave (the analog of the reflected plane wave). It propagates along the – ρ axis.
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