A modified reciprocal equation to predict the complex transmission coefficient of a flow duct

Reciprocity is a basic property existing in wave phenomena characterized by complex transmission coefficients. duct describes the relationship between direct response at outlet to source applied inlet and reverse outlet. The reciprocity has been adopted simplify methodology for predicting coefficient from vice versa. methods, however, cannot predict form of because they only consider moduli but neglect phases. study on with temperature gradient hardly seen. present work derived reciprocal equation time domain method characterize spatially varying temperature. In addition considering coefficients, proposed invented correction term their phases as well. was developed delay incident transmitted pulses solved method. modified using used calculating exhaust noise an engine connecting duct. result shown that effective approach accurately describe phase waves flow ducts.