Sound insulation of the plane end walls of a semicylindrical housing

Abstract

In our previous work [1] a problem is solved for estimation of sound insulation R_c – the lateral wall of the housing on condition that edges are rigid and do not transmit the sound. This is not always accomplished in practice, therefore when designing a question concerning the choice of the parameters of the ends so that they would not worsen R_c comes into forth. In this paper a problem will be considered on the sound insulation of an end wall by making a assumption that an end wall is rigid. In this work also a frequency case will be considered when a point source is located on the axis of a semicylinder.
The problem is solved by series expansion of the sound pressure p₁ inside the housing and the flexural displacement of the wall u in eigenfunctions of the boundary value problem.