Closed form solutions for the acoustical impulse response over a masslike or an absorbing plane.
Closed form solutions for the acoustical impulse response over a masslike or an absorbing plane.
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DOI：
10.1121/1.3570947
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发表时间：
2011-06
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影响因子：
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通讯作者：
M. Ochmann
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文献类型：
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作者：
M. Ochmann
在无限局部反应平面上由狄拉克脉冲函数引起的瞬态声场可以通过在频域对相应的半空间格林函数进行傅里叶反变换来计算。作为起点，Ochmann [J]给出的表示。Acoust。Soc。使用Am. 116(6), 3304-3311(2004)]，它由点源的离散和连续叠加组成。对于具有类质量特性和纯吸收特性的局部反应平面，可以用封闭形式表示得到的脉冲响应。这样的结果是令人惊讶的，因为在频域中还没有相应的公式。因此，第一个主要结果是具有纯虚阻抗的无限平面上的脉冲响应的封闭形式解Eq.（22）。第二个主要结果是具有纯实阻抗的无限平面上的脉冲响应的封闭形式解Eq.（53）。作为这两个主要结果的特殊应用，卷积技术用于导出具有一般时间依赖性的点源的公式。对于特殊的信号，如指数衰减的时间信号或三角形脉冲，产生的声场可以用初等函数表示。
The transient sound field caused by a Dirac delta impulse function above an infinite locally reacting plane can be calculated by applying the inverse Fourier transform of the corresponding half-space Green's function in frequency domain. As a starting point, the representation given by Ochmann [J. Acoust. Soc. Am. 116(6), 3304-3311 (2004)] is used, which consists of discrete and continuous superposition of point sources. For a locally reacting plane with masslike character and also with pure absorbing behavior, it is possible to express the resulting impulse response in closed form. Such a result is surprising, because corresponding formulations in the frequency domain are not available yet. Hence, the first main result is the closed form solution Eq. (22) for an impulse response over an infinite plane with a pure imaginary impedance. The second main result is the closed form solution Eq. (53) for an impulse response over an infinite plane with a pure real impedance. As a particular application of both main results, a convolution technique is used for deriving formulas for point sources with a general time dependency. For special signals like an exponentially decaying time signal or a triangular shaped impulse, the resulting sound field can be presented in terms of elementary functions.