Vibro-acoustic analysis of wind instruments with membranes on resonance holes

Abstract

Some Asian wind instruments have a membrane glued over a special hole. A Japanese flute “Shino-bue” has a special hole called “resonance hole” between the mouth-hole and the first tone-hole. The resonance hole is covered with a bamboo paper membrane called “Chikushi”. “Dizi” in China and “Taegum” in Korea also have a similar structure. The vibration of the membranes gives the wind instruments their characteristic bright timbre, thereby making them distinctive from comparable Western instruments. To investigate the influence of the membrane upon acoustical properties of such a wind instrument more qualitatively, this paper develops a numerical method for calculating the sound field around a wind instrument with a membrane on its resonance hole, as a vibro-acoustic system. This method couples, the integral equation derived from the normally differentiated Kirchhoff-Huygens formula for the sound field around the thin obstacle, with a theoretical solution of the vibration equation for the membrane. The formulation of the developed method is confirmed by comparing numerical results with measured results for a simple model of the wind instrument. Effects of the tension of the membrane, the size and location of the resonance hole, are discussed through numerical calculations using the developed method.