Semi-analytical acoustic solution for the propagation of plane sound waves in a varying area duct for isentropic and non-isentropic cases are presented. The duct also sustains a mean flow and axial gas property gradients. A second order differential equation(ODE) in frequency domain is obtained from linearised Euler equations, upon neglecting the communication between acoustic and entropy disturbances, for each case. This ODE, with varying coefficients, is solved using adaptive WKB approximation technique, and the obtained wave-like solution consist of an asymptotic expansion, expressed as superposition of downstream and upstream propagating wave components. Frequencies considered here are not very high to assure that acoustic field is predominantly one-dimensional and diffusive effects are negligible, but large enough for WKB to be valid. Two industrial gas turbine combustor outlet converging sections with a temperature gradient and a high mean-flow acceleration are considered as test cases. Analytical results are compared to two numerically solved solutions: (1) three linearised Euler equations(3LEE), considering acoustic-entropy coupling; (2) two linearised Euler equations(2LEE) assuming acoustic and entropy waves as independent, and thus effect of entropy disturbance is also studied. Semi-analytical solutions agree well with 2LEE results in low mach-number regions when Documaci's limiting frequency criteria are satisfied.