• 物理实验 •

### 弦、杆、环的横振动理论与实验研究

1. 中山大学物理学院 物理学国家级实验教学示范中心,广东  广州510275
• 收稿日期:2022-09-15 修回日期:2022-10-14 出版日期:2023-07-01 发布日期:2023-07-06
• 通讯作者: 沈韩，Email: shenhan@mail.sysu.edu.cn
• 作者简介:方奕忠(1969—)，男，广东开平人，中山大学物理学院高级实验师，博士，从事理论物理及大学物理实验教学与研究工作
• 基金资助:
国家自然科学基金(61871410)、中山大学质量工程项目（中山大学教务〔2022〕20号，74130-12220011）资助

### Theoretical and experimental study of transverse vibration of string, beam and ring

FANG Yi-zhong, CUI Xin-tu, SHEN Han, HUANG Zhen-cheng,  FENG Rao-hui, LIAO De-ju, PANG Xiao-ning

1. National Demonstration Center for Experimental Physics Education, School of Physics,
SunYat-sen University, Guangzhou, Guangdong 510275, China
• Received:2022-09-15 Revised:2022-10-14 Online:2023-07-01 Published:2023-07-06

Abstract: From the strict derivation of transverse vibration of string, the explicit solution of wave velocity is obtained. Through measuring the wavelength and eigen frequency of resonance, the experiment value of wave velocity is also obtained, which is well agreed with the theoretical value. The transverse vibration equation of beam is also solved exactly. The simulation of the problem which one end is clamped and the other is free, is performed. The expressions of first several resonant eigen frequencies and the sites of standing-wave nodes are obtained so as to get the general solution. Further, the fundamental frequencies and resonant frequencies of the previous order overtone of steel slender strips under different lengths are measured. The co-ordinates of standing-wave nodes are observed and equivalent to the theoretical results, and the Young’s modulus of the strips are calculated, which are well corresponded with standard values. Furthermore, the case of small radial vibration of ring is popularized. The resonant frequencies and wavelengths are also measured, and the elastic modulus of circular cross section ring are obtained, where are also accorded with the existing values.