“…Approximate expressions for inlet radiation have been developed in terms of mode cutoff ratio _ 'fr1/ a mn y 1-MD where the dimensionless frequency Ti= f D/c; with the eigenvalue of the (m,n)th mode, a mn; duct diameter, D; duct Mach number, M D ; and speed of sound, c. The key simplification realized by the cutoff ratio formulation is that modes with the same C and p propagate similarly to the far field. This has been demonstrated for radiation from a flanged duct without flow (63) and is fairly accurate for principal lobe radiation (64). Two important duct mode propagation angles, ¢ x and ¢ x , are defined in (65) Here, ¢ x and q) x are the angles which the vector normal to the wave front and the group velocity vector, respectively, make with the duct axis.…”