Abstract: The analytical solution of Chladni figures on a thin mental board is a hard nut to crack in theoretical acoustics.When the boundary of a board is clamped or simply supported,the question can be solved quite completely,but in the condition of free boundary,the solution becomes rather difficult.In this paper,the two-dimensional standing waves of a circular plate（ Chladni figures） in various frequencies are investigated experimentally and theoretically.It is found that the Chladni figures can be precisely controlled by adjusting the frequency and position of the vibration source.The patterns of three kinds have been observed,only having circular nodal lines,radial nodal lines and the combination of the two kinds of nodal lines,respectively.Furthermore,the wave vectors,phase velocities and the elastic modulus of the plate are also obtained.The results of experiments well correspond with the analytical solutions.

Key words: standing waves, m order Bessel equation, Chladni figures, circular plate