周回の積分方程式による2次元音場の解析I

抄録

An integral equation with respect to sound pressure on the periphery of a given two-dimensional area was formulised to analyze two-dimensional sound field. For that purpose, the Hankel function of the second kind was used as a Green's function and applied to Green's theorem. The equation was rewritten in a matrix equation and then numerically calculated by dividing the periphery of two-dimensional area into N sections. The eigenvalue for a rectangle surrounded by a rigid wall was first obtained. The relation between the number of sections N and the accuracy of the calculation was shown. The calculation was also carried out for five kinds of shapes varying from a rectangle to a violin frame. On the basis of the eigenvalues calculated for the two-dimensional sound field isolated from outside, the acoustic significance of the shape of a violin frame was discussed.