Investigation on the Edge Phenomena of Multilayer Sound Absorbing Panels

Abstract

The authors have indicated in a previous paper (1975) that the increase of sound absorbing power A_p per unit length of the edge is expressed by the next equation almost independently of wave number N and incident angles of sound wave A_p &ampsime 0. 12(r_a-r_b)^2λ where variable λ is the wavelength of the sound wave, and two single-layer sound absorbing panels whose amplitude reflection factors are r_a and r_b, respectively, are supposed. The main purpose of this paper is to expand the previous results to the case of multilayer sound absorbing panels and to clarify how the edge phenomena are formulated in this case. For this purpose, the authors have adopted a group of correlationless continuation of sine-waves of finite length as an incident wave form as in the previous paper. For this incident wave, general expressions for the sound pressure of the edge wave p_e(t, x_0) and for the normal component of the particle velocity of the edge wave v_e(t, x_0) are proposed. Utilizing these expressions general formulation for sound absorbing power density p(x_0) caused by the edge phenomenon has been derived. The authors also discuss the case where the characteristics of two sound absorbing panels are represented only by their dominant reflected waves, respectively. By the numerical integration of p(x_0) the sound absorbing power P_e(θ, φ) per unit edge length has been obtained. It is proved that the sound absorbing power P_e(θ, φ) is valid for the edge phenomena of more general multilayer sound absorbing panels, provided that the wave number N is taken as being sufficiently large. In the case that each of the parameters do not vary in accordance with the incident angles of the sound wave, and that a perfectly defusing sound field is assumed, it is shown that the increase of the sound absorbing power (A_p) is expressed by the equation A_p &ampsime 0. 1λ(r^2_a+r^2_b-2r_ar_bcosφ) where variable φ is the phase difference between each dominant reflected wave.