Beuth Hochschule für Technik Berlin - University of Applied Sciences, Department of Mathematics, Physics, and Chemistry, Luxemburger Strasse 10, 13353 Berlin, Germany.
J Acoust Soc Am. 2011 Jun;129(6):3502-12. doi: 10.1121/1.3570947.
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.
无限局部反应平面上方狄拉克 δ 脉冲函数产生的瞬态声场可以通过在频域中应用相应半空间格林函数的傅里叶逆变换来计算。作为起点，使用 Ochmann [J. Acoust. Soc. Am. 116(6), 3304-3311 (2004)]给出的离散和连续点源叠加的表示形式。对于具有质量特性且具有纯吸收行为的局部反应平面，可以以封闭形式表示所得脉冲响应。这样的结果令人惊讶，因为在频域中还没有相应的公式。因此，第一个主要结果是无限平面上具有纯虚阻抗的脉冲响应的封闭形式解式 (22)。第二个主要结果是无限平面上具有纯实阻抗的脉冲响应的封闭形式解式 (53)。作为这两个主要结果的特定应用，卷积技术用于推导出具有一般时间相关性的点源的公式。对于特殊信号，如指数衰减时间信号或三角形脉冲，所得声场可以用基本函数表示。
