Radiation and reflection in a rectangular cross-section waveguide: Finite difference simulation and theoretical frequency domain impedance

If a theoretical expression is known for the radiation impedance then it may be projected to predict the input impedance and input impulse response in an acoustic waveguide. Radiation impedance may be derived from integration of Green’s functions and so are based on continuous expressions in the frequency domain.

In this study the finite difference technique will be used to simulate the reflections of a band limited impulse as it travels down a horn and partially radiates and reflects from the end. The finite difference technique used here is based on approximating the 3 dimensional lossless wave equation using differences between adjacent grid points to calculate differentials. These calculations will be performed for a discretized 3D rectangular horn within a large discretized 3D box whose walls may be set to absorb incident energy.

The finite difference results will be used to create animations to visualise the pressure field at the point of partial reflection and transmission of a band limited impulse in the time domain. Frequency domain analysis will then be used to compare the results with those predicted by the frequency domain impedance techniques.