中文摘要：

提出了声学负反射的概念，以解释茅山军号声现象的物理机制。首先建立平面声波在周期台阶状边界上的反射模型，利用边界扰动的方法，给出了该问题的精确解。发现在共振区域，即周期结构间距和声波波长在同一量级时，只有小部分声能沿着镜面反射的方向反射，而大部分反射声能在入射方向的同一侧。特别在满足布拉格共振条件下，一些频带内的声音能全部沿逆入射方向返回。此现象类似于光学的闪耀光栅效应，称其为声负反射。应用此概念，给出了基于衍射近似的回声频谱与实验结果不符的原因，解释了为何在台阶前广场的中轴线上能听到最响亮的军号声。军号声的6个音符是由6组台阶相继反射而产生。根据光栅反射的特点，对于给定观测点，爆炸声丰富的频率成分中只有某些特定频率才能被接收到，周期台阶的空间滤波作用使得回声不再是原来的爆炸声。进一步证明了这些频率成简单的整数比，所以最终听到的是富有节奏感的军号声。利用光栅方程和具体的台阶数据，还预测了6个音符的基频和泛频，与实验测量符合较好。

英文摘要：

The mysterious “Maoshan Bugle”phenomenon,the clearly audible bugle-like sounds after a launched firecracker blast in the air about 39 m high in the square in front of the Southern Jiangsu Anti-Japanese War Victory Monument at Mount Maoshan in Jiangsu,China,has drawn attentions of architects and acousticians in the past two decades.In this report,we attempted to reveal the physical mechanism of bugle calls and proposed the concept of acoustic negative reflection to explain the phenomenon.First,a model of plane sound wave reflection from an infinite periodic rigid surface is built and rigorously solved using an exact method of variation of boundaries,especially in the resonance region where the sound wavelength is of the same order as the periodic spacing.Then,numerical calculation is performed for the model with its periodic unit being taken as regular steps.Attention is then paid on the singular phenomenon that most of the incident sound power is reflected to the side of incidence,rather than to the side of specular reflection.This is what we call the negative reflection of sound,which is similar to the effects ofnbsp;blazed grating in optics.We then show the mysterious bugle calls at Mount Maoshan are actually the negative reflections,which are most clearly heard on the central axis in front of the square.The six notes of the bugle call are a result of sound reflection from the six groups of steps in front of the monument,which serve as acoustic gratings. According to the characteristics of the grating reflection,only certain frequencies in the explosion spectrum can be re-ceived.We further proved that these frequencies are integer multiples of the fundamental.Thus people hear the echo much like the rhythmic sound of a bugle,instead of the explosive sound.The spectrum characteristic of the reflected sound is theoretically analyzed by using the grating equation,with the calculated fundamental and harmonic frequencies well fitting with the audio samples recorded on site.Finally,we discussed the possibilities o