Exact solution for the acoustical impulse response of a line source above an absorbing plane.
Exact solution for the acoustical impulse response of a line source above an absorbing plane.
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DOI：
10.1121/1.5054301
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发表时间：
2018-09
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影响因子：
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通讯作者：
M. Ochmann
中科院分区：
文献类型：
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作者：
M. Ochmann
无限平面上狄拉克δ函数激发的二维波动方程的解是半空间的二维脉冲响应。等效地，它可以被认为是由无限长线源在三维（3D）空间中产生的声场。对于三维点源，如果无限大平面具有类质量或纯吸收特性，则可以用封闭形式表示所得的脉冲函数。本文从吸收面上方的三维脉冲响应出发，求出了吸收地面上方线源的封闭解，该解由直接压力贡献和反射信号组成。反射因子R的解析表达式是本文的主要结果。R是阻抗、时间和空间坐标的简单代数函数。由具有一般时间依赖性的线源产生的声场可以通过卷积来构造。对于高斯信号，数值计算得到的压力。对于矩形脉冲，推导了三维和二维的解析解。数值计算结果的偏差是非常小的。
The solution of the two-dimensional (2D) wave equation excited by a Dirac delta function above an infinite plane is the 2D impulse response of the half-space. Equivalently, it can be considered as the sound field generated by an infinite line source in three-dimensional (3D) space. For a point source in 3D, it is possible to express the resulting impulse function in closed form if the infinite plane is characterized by a masslike or pure absorbing behavior. Based on the 3D impulse response above an absorbing plane, a closed form solution for a line source over absorbing ground is found. This solution consists of the direct pressure contribution plus a reflected signal. The analytical expression for the reflection factor R is the main result of the work. R is a simple algebraic function of impedance, time, and spatial coordinates. The acoustical field generated by a line source with a general time dependence can be constructed by convolution. For a Gaussian signal, the resulting pressure is computed numerically. For a rectangular pulse, an analytical solution in 3D and 2D is derived. The deviations from the numerically obtained results are very small.