Green’s functions for acoustic problems is the fundamental solution to the inhomogeneous Helmholtz equation for a point source, which satisfies specific boundary conditions. It is very significant for the integral equation and also serves as the impulse response of an acoustic wave equation. They are important for acoustic problems that involve the propagation of sound from the source point to the observer position. Once the Green’s function, which satisfies the necessary boundary conditions, is obtained, the sound pressure at any point away from the source can be easily calculated by the integral equation. The major problem faced by researchers is in the process of constructing these Green’s functions which satisfy a specific boundary condition. The aim of this work is to review some of these fundamental solutions available in the literature for different boundary conditions for the ease of analyzing acoustics problems. The review covers the free-space Green’s functions for stationary source and rotational source, for both when the observer and the acoustic medium are at rest and when the medium is in uniform flow. The half-space Green’s functions are also summarized for both stationary acoustic source and moving acoustic source, derived using the image source method, equivalent source method and complex equivalent method in both time domain and frequency domain. Each of these methods used depends on the different impedance boundary conditions for which the Green’s function will satisfy. Finally, enclosed spaced Green’s functions for both rectangular duct and cylindrical duct for an infinite and finite duct is also covered in the review.

中文翻译：

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格林函数对声学问题的简要调查

声学问题的格林函数是满足特定边界条件的点源非齐次亥姆霍兹方程的基本解。它对于积分方程非常重要，也可以作为声波方程的脉冲响应。它们对于涉及声音从声源点传播到观察者位置的声学问题很重要。一旦得到满足必要边界条件的格林函数，就可以很容易地用积分方程计算远离声源任意点的声压。研究人员面临的主要问题是在构建这些满足特定边界条件的格林函数的过程中。这项工作的目的是回顾文献中针对不同边界条件可用的一些基本解决方案，以便于分析声学问题。该评论涵盖了自由空间格林函数对于固定声源和旋转声源，适用于观察者和声学介质静止时以及介质均匀流动时的情况。还总结了静止声源和移动声源的半空间格林函数，分别在时域和频域使用图像源法、等效声源法和复等效法推导。使用的这些方法中的每一种都取决于格林函数将满足的不同阻抗边界条件。最后，