A transformation is described which relates the sound generated by low Mach number flow to the flow vorticity. For compact flow fields the apparent sound source is of quadrupole type and linear in the vorticity and therefore also linear in the flow velocity. This scheme is applied to the sound generated by the interaction of two identical thin vortex rings. Then a flow field with a number of compact vortices is discussed. It is found that each vortex can be replaced acoustically by a dipole related to the impulse of the vortex, plus the quadrupole just mentioned plus a spherically symmetric sound source related to the energy of the vortex. An application to low Mach number free-space turbulence shows that the generated sound is related to the vorticity correlation tensor.

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A sound wave propagating in an inhomogeneous duct consisting of two semi-infinite uniform ducts with a smooth transition region in between and which carries a steady flow is considered. The duct walls may be rigid or compliant. For an irrotational sound wave it is shown that the three properties of the title are closely related, such that the validity of any two implies the validity of the third. Furthermore it is shown that the three properties are fulfilled for lossless locally reacting duct walls provided the impedance varies at most continuously. For piecewise-continuous wall properties edge conditions are essential. By an analytic continuation argument it is shown that reciprocity remains true for walls with loss. For rotational flow, energy conservation theorems have been derived only with the help of additional potential-like variables. The inter-relation between the three properties remains valid if one considers these additional variables to be known. If only the basic gasdynamic variables in both half-ducts are known, one cannot formulate an energy conservation equation; however, reciprocity is fulfilled.

A study of the scattering matrix S of sound waves propagating in an inhomogeneous duct which consists of two semi-infinite ducts, connected somehow, is undertaken. The scattering matrix contains all reflection and transmission coefficients from the nth into the mth propagating mode for upstream and downstream propagation. A mean flow u0 is included. From energy conservation one finds, that S is unitary for potential flow, SS+=E, if the mode normalization is performed to unity energy flux. Invariance considerations with respect to time reversal reveal that S* (ω, −u0), the conjugate complex of the reverse flow scattering matrix, obeys the relation S* (ω, −u0) S (ω, u0) =E. From these two results, the reciprocity relation ST(ω, −u0) =s (ω, u0) is obtained, where ST denotes the transpose of S. Some implications of these results for sound waves propagating in potential flow are discussed. The modifications which occur in rotational flow are also described.

A semi-analytical theory for the scattering of plane sound waves by a compressible, non-homentropic, circular-cylindrical, single vortex is presented in this paper. As a special case, the scattering of sound by a cylindrical inhomogeneity (hot spot) is investigated. Contrary to the otherwise analogous quantum-mechanical scattering problem, there are singularities in the modified acoustic wave equation for radii xs ∈ (0, ∞) when the scattering by a vortex is considered. It will be shown how these singularities can be treated.This sound-scattering theory is applied to the problem of the interaction of weak plane shock waves with a strong cylindrical vortex. The calculated scattered sound signal has a rather complicated structure in which a cylindrical wave with an essentially quadrupolar directivity pattern is discernible. In the case of shock–hot-spot interaction a scattered sound signal with dipole-like amplitude is obtained. Both results qualitatively agree with experimental findings.