Recent experiments by Laufer and Yen offer the first chance yet for an examination in all detail of the predictions of Lighthill aeroacoustic theory. The experiments concern the internal flow structure and radiated acoustic field of discrete tone subharmonic instability waves associated with multiple vortex interactions on the laminar initial shear layer of a weakly excited round air jet at very low Mach number (0.05 < Mj < 0.2). This paper will review all aspects of low Mach number aeroacoustic theory in the light of these experiments. Linear and nonlinear hydrodynamic stability theory will be used to give a reasonable description of the subharmonic shear layer waves. However, what should then follow as a routine application of the Lighthill theory throws up several difficulties, from which it is concluded that the theory apparently cannot be used in its elementary form to predict the sound from air jets even with Mach numbers as low as 0.1. [Work carried out in collaboration with Dr. Patrick Huerre, Dept. of Aerospace Engineering, Univ. of Southern California.]