Development of a General Procedure to Formulate Four Pole Parameters by Modal Expansion and Its Application to Three-Dimensional Cavities

Abstract

If an acoustic system has one or more large dimensions compared to the shortest wave length of interest, the pressure responses which are necessary to formulate four pole parameters have to be obtained by solving the continuous wave equation of the system. In this paper, a general procedure is established to derive four pole parameters from the pressure response solutions utilizing modal series expansion. As an example, four pole parameters of a cylindrically annular cavity are obtained. The validity of the procedure is proven by applying it also to a one-dimensional pipe whose four pole parameters are available by direct method. The comparison is made in terms of four pole parameters and pressure profiles along the pipe. The comparison allows interesting observations with regard to the equivalence of the two approaches. The theory was further generalized to be applied to more complex acoustic systems, namely multiply connected systems. A cylindrically annular cavity connected by two pipes to a small lumped parameter cavity is taken as an example of the application. Noise control by either mode cancellation or wave cancellation is explored.