The interaction of a plane sound wave with a compressible fluid rotating about an axis in the form of a Rankine vortex is considered for the case of small Mach numbers. It is shown that when the frequency of the sound wave is close to that of the rotating core of the vortex, resonance is generated in the vortex core. Resonance is also possible when the frequency of the sound wave is a multiple of the frequency of the rotating core. The amplitude of the scattered wave is reexamined and it is shown that in some limiting cases the details of some published material are inaccurate.