“水鸣天梯”声景观成因分析

Acoustic analysis of calling drip phenomenon

基于周期台阶表面声阻抗理论,解释了"水鸣天梯"声景观的物理机制。首先在低频准平面波近似的情况下,利用阻抗转移公式得到了周期台阶单元表面声阻抗。数值解表明,在低频段台阶表面的声阻抗呈现纯容抗性,证实了表面波的存在。有限元软件仿真的结果与理论分析保持一致。应用表面波的性质,设计并进行了现场试验。试验数据分析表明:在台阶底部脚踏石阶或者发射脉冲声波,声波经过台阶表面作用,到达台阶顶部时只有低频部分的声能量得到了较大保留,与理论分析和模拟结果相一致,最终确定了正是周期台阶的表面波滤波效应使得脚踏声转变为悦耳的水滴声。

The mysterious ＂calling drip＂ phenomenon that a series of clearly audible drip-like sounds could be heard at the top of stone steps after a footstep at the bottom, appearing at Crane Mountain in Qingdao has drawn attentions of tourists and acousticians in the past years. In this paper, we attempt to reveal the physical mechanism of ＂calling drip＂ by following the acoustic impedance of the periodic rigid surface. Under the quasi-plane wave approximation of low frequency, the numerical solution to the acoustic impedance of a single periodic stone step is obtained by using the transfer impedance function. At low frequency, the acoustic impedance of stone steps＇ surface presents pure acoustic reactance, which supports the existence of surface waves. And the finite element simulation is consistent with the theoretical analysis. Experiments are designed and performed by using the properties of surface waves. The analysis results of the experimental data show that, only the low-frequency part of sound energy is greatly preserved when the footstep at the bottom or the pulse along the surface of stone steps reaches the top, which is consistent with the theoretical analysis and simulation. In the end, we determine that it is the surface wave filtering effect of periodic steps makes the footstep change into a melodious drip-like sound.