Chladni plates sing purely only when one mode alone is excited

Evidence

What miracle analogous to the Helmholtz kink on a bowed string might happen when a metal plate is bowed? Why should a Chladni plate, possessing many inharmonic mode frequencies, set up a cooperative resonance when bowed? How sticking and slipping works with a bow and a Chladni plate is not so clear, since in the pure sinusoidal mode there is no sawtooth Helmholtz kink wave to follow the bow in the sticking phase and jerk away suddenly in the slip phase. The bowing of a Chladni plate is tricky to do, nothing like the near certainty of a well-rosined bow on a string. Like a clock that has run down and is correct only once per day (on the 24-hour system), a sinusoidal oscillation will be going at just the right speed to stick to the bow at only one instant per oscillation. In reality, there is probably a short time interval over which the bow sticks, made possible by the elasticity of the horsehairs. During that interval, a little energy can be put into the vibration. With some practice or luck, it is possible to get the plate “singing” at one pure frequency, signaling the excitation of a single mode. This is facilitated by holding a thumbnail on the edge of the plate, at a position where the desired mode has a node, damping the other modes, and making the choice of a mode to cooperate with easier. Unless only one mode is excited, the sand will not find nodal lines to rest in, only points or segments shared by the several excited modes. The resulting sound is purely sinusoidal: a pure tone, even though the pattern of vibration and the nodal lines on the surface may be complex. — Eric J. Heller, Why You Hear What You Hear- An…, 1399

Categorization

• QUESTION: The stick-slip mechanism for bowing a plate lacks a Helmholtz kink analog - worth investigating how the horsehair elasticity window sustains oscillation.
• XREF: Connects to Helmholtz kink mechanics and the clock metaphor used in chapter 18 on bowed strings.