以平面薄膜自由振动的理论研究为基础，结合第八届全国大学生物理学术竞赛题目，研究汽笛振动发声的现象，根 据圆膜自由振动方程使用贝塞尔函数求解，分析出圆膜振动的不同模态.通过使用3D 打印技术制作不同规格的汽笛圆管改变 实验条件，利用高速摄像机记录圆膜振动过程，使用Audacity 软件分析圆膜振动基频，实现了对圆膜振动的定量研究.研究结 果表明，在圆膜弹性形变处于线性区间内，圆膜在振动中所受张力的大小是影响振动模态选择的主要因素，且在同种振动模 态中，改变汽笛圆管的长度和内径对振动形式无影响.

Based on the theoretical study of free vibration of plane film，combined with the Eighth National College Physics academic competition，the phenomenon of sound vibration of the whistle is studied. According to the free vibration equation of the circular film，the different modes of the circular film vibration are analyzed by using the Bessel function. We make the 3D printing technology to make different specifications of the whistle. The circular tube changes the experimental condition，we use a high-speed camera to record the vibration process of the circular film，and use the Audacity software to analyze the fundamental frequency of the circular film vibration. The quantitative study of the vibration of the circular film is realized. The results show that the size of the tension of the circular film in the vibration is the choice of the vibration mode in the linear interval of the elastic deformation of the circular film. The main factor is that in the same vibration mode，changing the length and inner diameter of the whistle tube has no effect on the vibration form.