大学物理 ›› 2019, Vol. 38 ›› Issue (9): 54-.doi: 10.16854 /j.cnki.1000-0712.190046

• 大学生园地 • 上一篇    下一篇

低频条件下的法拉第斑图选择问题研究

亓瑞时,王海粼,王伟,周路群   

  1. 北京大学物理学院,北京100871
  • 收稿日期:2019-02-01 修回日期:2019-03-28 出版日期:2019-09-20 发布日期:2019-10-17
  • 通讯作者: 周路群,E-mail: zhoulq22@ pku.edu.cn
  • 作者简介:亓瑞时( 1998—) ,男,山东泰安人,北京大学物理学院2016 级本科生.

Pattern selection of Faraday waves at lower frequencies

QI Rui-shi,WANG Hai-lin,WANG Wei,ZHOU Lu-qun   

  1. School of Physics,Peking University,Beijing 100871,China
  • Received:2019-02-01 Revised:2019-03-28 Online:2019-09-20 Published:2019-10-17

摘要: 在一定条件下,受到竖直方向周期性驱动力作用的液体自由表面会产生特定的驻波图样,即法拉第斑图. 本实验以圆柱形容器中的黄原胶溶液为研究对象,利用模态激振器驱动容器所在的平台,并通过高速摄像机捕获法拉第斑图图样,探究了低频条件下的斑图选择问题. 实验结果显示,在一定的参数条件下,在斑图出现的临界点附近有一弱非线性区,这一区域内许多实验现象都可以利用线性振动的理论近似解释. 此时形成的斑图往往仅分布于容器的一条直径上,随着驱动力频率的增大,所形成的波腹数目增加,斑图稳定性交替变化. 理论分析表明,这一现象是表面驻波色散关系和容器边界条件共同作用的结果.

关键词: 法拉第斑图, 色散关系, 斑图选择问题

Abstract: Under certain conditions,specific nonlinear standing waves would form on the free fluid surface subjected to a vertical oscillation,termed Faraday waves. In this experiment,xanthan gum solution in a cylinder container is took as the research object,and the pattern selection problem at lower frequencies is explored. A vibration exciter is used to drive the platform where the vessel is placed and a high-speed camera is employed to catch the images of the Faraday waves. The experimental results have shown that under certain parameters,there exists a weakly nonlinear region near the onset value at which many experimental phenomena could be explained approximately by the linear vibration theory. In this region the pattern is usually located only along one of the diameters of the container. The number of antinodes increases with the frequency of the driving force increasing and the stability of the pattern changed alternately. Theoretical analysis shows that this phenomenon is resulted from the interaction of the dispersion relation and the container boundary conditions.

Key words: Faraday waves, dispersion relation, pattern selection