Lighthill's theory of aerodynamic noise has been the foundation of the current noise research. The theory is exact and based on an acoustic analogy. The source strength, however, can be found only when the problem is solved. To make a quantitative calculation, one has to make various approximations to the theory. The present study provides a critical evaluation of these approximations, Based on a matched asymptotic method, Navier-Stokes equations are expanded in Mach number. To the first order, the flow field (M2) is generally nonisentropic. The pressure is generated by the incompressible Reynolds stresses in the flow and the normal stress and velocity fluctuation on the surface. The acoustic field (M5) is obtained by matching with the flow field. Acoustic pressures in both stationary and moving media are obtained. Surprisingly, the first-order noise generation does not depend upon the thermal and entropy effects in the flow and the shear stress on the surface. Comparisons with previous works and discussions of possible new approaches on aerodynamic noise are made.