On sound propagation from a slanted side branch into an infinitely long rectangular duct

Abstract

The transmission of sound from a slanted side branch into an infinitely long rectangular duct is studied numerically using the method of finite element with absorptive domain exit boundaries. The sound transmission coefficients associated with various acoustic modes are investigated in details. The results show that the plane wave assumption is only valid at very low frequency. It is also found that the intensities of the higher modes are stronger than that of the plane wave once they are excited. Besides, a critical side-branch slant angle is found over which a significant change of sound propagation mode takes place. This affects substantially the energy distribution between various acoustic modes inside the main duct. A simplified model is proposed to explain the phenomenon and the relationship of this critical angle with the width ratio between the side branch and the main duct is established.