Numerical simulation and analytical solution for plane waves focused by a parabolic reflector

A transient analytical solution is presented to predict the pressure responses along the axis of a parabolic reflector for normally incident plane waves. The solution was derived using geometrical acoustics and the Kirchhoff-Helmholtz integral. Results of the analytical solution were compared to the numerical simulation results, and good agreements were obtained. The numerical simulation visualizes the wave field in air to give a better understanding of propagation of the reflected waves.