Homogenisation theory is used to derive Wood’s formula for the speed at which a pressure wave can propagate in an air/water mixture. The smallness of the impedance ratio between air and water results in a dramatic lowering of the wave speed of the mixture and, when the air fraction is small, the possibility of regions of persistent ringing in the vicinity of the boundary where the pressure is applied. Only Goupillaud media are considered and, for the periodic case, the asymptotic predictions are validated against exact numerical calculations. An example in which the air/water layers vary randomly is also presented.

中文翻译：

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空气/水混合物中的一维声波

均质化理论用于推导出压力波在空气/水混合物中传播的速度的伍德公式。空气和水之间的阻抗比小会导致混合物的波速显着降低，并且当空气比例小时，在施加压力的边界附近可能会出现持续振铃的区域。仅考虑 Goupillaud 介质，对于周期性情况，渐近预测会根据精确的数值计算进行验证。还提供了空气/水层随机变化的示例。