A possible medium is considered with a large number of diverse but possibly similar relaxation processes. The equations for single spatially located relaxation processes of general type are developed and extended to a large spatially extended system. Each process is characterized by a relaxation time and a relaxation strength and is excited by the local pressure in an incident acoustic wave. A constant frequency model is initially assumed with complex amplitudes associated with acoustic pressure and relaxation responses. A smearing process results in the collective relaxation responses being regarded as a continuous function of relaxation times. An expression for entropy perturbation is developed in terms of the relaxation responses. The equations of fluid mechanics then lead to an expression for the pressure perturbation in terms of the dilatation and the relaxation processes. The extended result yields a time-domain wave equation for propagation through an inhomogeneous medium with distributed relaxation processes. Expressions for frequency-dependent attenuation and phase velocity are derived in which relaxation is characterized by a single function giving strength as a continuous function of relaxation time. Possible choices for this function are discussed, and it is shown that some choices lead to an attenuation varying nearly as a power of the frequency over any fixed and possibly large range of frequencies. A model set of parameters leads to good agreement with attenuation and phase velocity measurements for a suspension of human red blood cells in saline solution, as communicated to the authors by Treeby and analogous to those reported by Treeby, Zhang, Thomas, and Cox.

中文翻译：

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具有空间分布弛豫过程的介质中的声传播和频率幂律衰减的可能解释

一种可能的介质被认为具有大量不同但可能相似的松弛过程。一般类型的单个空间定位弛豫过程的方程被开发并扩展到一个大型空间扩展系统。每个过程都以弛豫时间和弛豫强度为特征，并由入射声波中的局部压力激发。最初假设恒定频率模型具有与声压和弛豫响应相关的复振幅。涂抹过程导致集体松弛响应被视为松弛时间的连续函数。根据松弛响应开发了熵扰动的表达式。然后，流体力学方程根据膨胀和弛豫过程得出压力扰动的表达式。扩展结果产生了一个时域波动方程，用于通过具有分布弛豫过程的非均匀介质传播。推导了频率相关衰减和相速度的表达式，其中弛豫的特征在于单个函数，该函数将强度作为弛豫时间的连续函数。讨论了该函数的可能选择，并且表明某些选择导致衰减几乎作为频率的功率在任何固定和可能的大频率范围内变化。一组模型参数与盐溶液中人红细胞悬浮液的衰减和相速度测量值具有良好的一致性，