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We study the scattering of first and second sound waves by quantum vorticityin superfluid Helium using two-fluid hydrodynamics. The vorticity of thesuperfluid component and the sound interact because of the nonlinear characterof these equations. Explicit expressions for the scattered pressure andtemperature are worked out in a first Born approximation, and care is exercisedin delimiting the range of validity of the assumptions needed for thisapproximation to hold. An incident second sound wave will partly convert intofirst sound, and an incident first sound wave will partly convert into secondsound. General considerations show that most incident first sound converts intosecond sound, but not the other way around. These considerations are validatedusing a vortex dipole as an explicitely worked out example.Comment: 24 pages, Latex, to appear in Journal of Low Temperature Physic

Scattering of first and second sound waves by quantum vorticity in superfluid helium