The application of Kirchhoff's formula to the numerical calculation of transient response in an enclosure

Abstract

This paper is concerned with the use of Kirchhoff's time-retarded potential boundary integral equation in the numerical calculation of the transient response in an enclosure with rigid or absorbent boundary. The sound pulse reflected from the absorbent boundary, consisted of a porous layer on a rigid backing, is calculated by using the time-dependent “impulse admittance” (inverse Laplace transform of the normal admittance). Next, the numerical integration method of Kirchhoff's integral equation and some problems arising in the calculation are discussed. Finally, transient responses for a rigid and an absorbent cubic rooms are calculated numerically by Kirchhoff's integral equation and compared with the precise results given by the image sources method.