The factors which affect the sound production of a vortex as it passes through a nozzle are investigated at both low and high Mach numbers using time-accurate inviscid-flow computations. Vortex circulation, initial position, and mean-flow Mach number are shown to be the primary factors which influence the amplitude and phase of the sound produced. Nozzle geometry and distribution of vorticity are also shown to play significant roles in determining the detailed form of the signal. Additionally, it is shown that solution bifurcations are possible at sufficiently large values of vortex circulation. Comparisons are made between sound signals computed directly using a numerical method for the Euler equations and predictions obtained using a compressible vortex-sound analogy coupled with a compact-source assumption for the computation of vorticity dynamics. The results confirm that the latter approach is accurate for a range of problems with low mean-flow Mach numbers. At higher Mach numbers, however, the non-compactness of the source becomes apparent, resulting in significant changes to the character of the signal which cannot be predicted using the analogy-based approach. Implications for the construction of simplified models of vortex sound in solid-rocket nozzles are discussed.