The mathematical theory of vibrating membranes or plates, which is usually applied to squares and rectangles, may also be used for triangles provided the equations are plotted on axes which are not rectangular. These triangles are then fitted together to produce many sided symmetrical plates. Thus the Chladni patterns are found mathematically for polygonal membranes or plates. If one angle of the triangle is made very small, the plates are practically circular so that these equations also give the patterns on circular plates (approximately) for special cases. The triode valve oscillator which drives the plates is calibrated accurately so that the frequency of the plates is found at the time the patterns are formed. A table gives a comparison between the observed and calculated frequencies.
It is shown that Kirchhoff's solution for a circular plate is a special case which gives circles and diameters only. If this solution is generalized, the very intricate figures actually found upon circular plates may be calculated mathematically. In particular, a few figures found by Chladni are computed from the new equations. The methods of computation from the curves of the Bessel functions are outlined briefly.
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