压缩驱动单元中声波本征值问题的解析解

解析法求解了号筒扬声器压缩驱动单元中振膜和相位塞间空腔内声波的本征振动问题,该问题表现为既带有θ=0处的自然边界条件又带有空腔边缘的第二类齐次边界条件的勒让德方程.采用在正则奇点θ=0展开级数的方法,得到了幂级数形式的解析解.进一步将该方程转换为零阶贝塞尔方程,给出了近似解.2种解法结果相当吻合.

Analytical solution for eigenvalue problem of sound wave in compression driver

The eigenvalue problem of sound wave in the cavity between phase-plug and membrane in a compression driver of a horn was solved analytically,which was described by the Legendre equation with both the natural boundary condition at θ = 0 and a second homogeneous boundary condition at the edge of the cavity.The analytical solution was obtained in terms of the power series expanded at the regular singular point θ = 0.Further more,the Legendre equation was transformed into the zero-order Bessel equation,and the approximate solution was therefore obtained. It was showed that the results from the two solutions agreed very well.