We propose a modified Kuramoto model to describe the hand-clapping synchronization observed in a large group of people. There are two different ingredients in our model: The finiteness of the sound speed leads to the time-delay effect across the system, and the large distance makes the sound intensity decrease significantly. These two different but related factors are expected to make the synchrony in a large audience hard to achieve. We numerically and analytically test which between the two factors can be crucial to explain the failure of hand-clapping synchronization in a large group of people. We conclude that the time-delay effect due to the finite sound speed is not as important as the effect of the decreasing sound intensity with distance as long as the audience size is not too big.

我们提出了一个改进的 Kuramoto 模型来描述在一大群人中观察到的拍手同步。我们的模型中有两个不同的成分：声速的有限性导致整个系统的时延效应，距离大使声强显着降低。预计这两个不同但相关的因素将使大量观众的同步难以实现。我们通过数值和分析测试这两个因素之间的哪一个对于解释一大群人拍手同步失败至关重要。我们得出的结论是，只要观众规模不是太大，由于有限声速引起的延时效应不如随距离减小的声强效应重要。