Singular points of intensity streamlines in two-dimensional sound fields

Continuing earlier work on this subject, a more rigorous discussion is given of the singular points of streamlines and the critical points of the stream function. The results for vortex and saddle points obtained earlier in piecemeal fashion and by way of examples are obtained systematically and by generally utilizing the applicable theory of differential equations and calculus. New results are also obtained. For example, a saddle point can occur when the phase of pressure and velocity differ by π/2, and in certain parts of the sound field, specifically inside a closed streamline, the number of vortex points and saddle points are related. Finally, the streamlines and singular point are considered for a discrete source: the line source.