In cylindrical and spherical geometries, the proper linear combination of standing waves results in a rotating wave field. Such a field looks like a traveling wave chasing its tail: a constant field rotating in space. These rotating wave fields can be considered to be a third major category of waves, similar to traveling and standing waves. While all three types of waves are interrelated, rotating waves offer the clearest insight into angular momentum and rotary motion in wave fields. This paper summarizes the field equations and physics for various rotating wave fields and goes on to discuss simple demonstrations of rotating waves on the surface of water.

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