The forced sound transmission of finite single leaf walls using a variational technique

Abstract

The single wall is the simplest element of concern in building acoustics, but there still remain some open questions regarding the sound insulation of this simple case. The two main reasons for this are the effects on the excitation and sound radiation of the wall when it has a finite size, and the fact that the wave field in the wall is consisting of two types of waves, namely forced waves due to the exciting acoustic field, and free bending waves due to reflections in the boundary. The aim of the present paper is to derive simple analytical formulas for the forced part of the airborne sound insulation of a single homogeneous wall of finite size, using a variational technique based on the integral-differential equation of the fluid loaded wall. The so derived formulas are valid in the entire audible frequency range. The results are compared with full numerical calculations, measurements and alternative theory, with reasonable agreement.

The average specific forced radiation wave impedance of a finite rectangular panel

“…It is often necessary to increase the maximum number of iterations or decrease the precision. As observed by Brunskog (2012), Eq. (12) is much more efficient numerically than Eqs.…”

“…It occurs naturally when variational techniques are used to solve these phenomena (Thomasson, 1980(Thomasson, , 1982Allard and Atalla, 2009;Brunskog, 2012;Jeong, 2013). Thus, this average value can be viewed as the one sided specific radiation wave impedance fluid loading on a two dimensional transverse velocity wave which is propagating on a finite plane surface mounted in an infinite rigid baffle.…”

In situ measurements of the oblique incidence sound absorption coefficient for finite sized absorbers

“…3,4,12 This can be seen if studying Ref. 18, where the corresponding theory is applied to a plate in bending, which is non-locally reacting. In the present case, when expressing the admittance as an differential operator Bfpg, this will be converted into an ordinary linear admittance if the pressure field is a projected plane wave Bfpe Àjðk x xþk y yÞ g ¼ bðk x k y Þpe Àjðk x xþk y yÞ .…”

“…(15) is not well suited for numerical integration. Thus, a numerically more convenient expression with just two integrals, following the procedure described by Brunskog, 18 based on a variable substitution, 21 is given by…”

The acoustic radiation impedance of a rectangular panel

“…It occurs naturally when variational techniques are used to solve these phenomena [1,2,7,8]. The normalized real part of the acoustical radiation impedance of one side of a finite rectangular panel mounted in an infinite rigid baffle is also the panel's one sided acoustic radiation efficiency.…”