One of the two initial kinks seeds and reinforces the Helmholtz mode.

Evidence

Why does a Helmholtz mode form on the string in the first place? This is a central question for one of the most important nonlinear, cooperative resonances in all of musical sound. Certainly, a kink is ideal for initiating a single sticking and slipping cycle in each period. In turn, the sudden jolts imparted by catching and releasing the string tend to form kinks. In the first moments of an up-bow, the string is dragged along while sticking to the bow, but ultimately the restoring force of the string overwhelms and the string slips suddenly. This initial sudden release can be modeled in Falstad’s Loaded String applet, by plucking the string at a point. Two kinks will fly away from that point, one in each direction. If nothing else happened, these two kinks would rejoin one period later after two reflections each. These are not yet the Helmholtz wave, but one of the kinks (the one traveling counterclockwise for the up-bow) is the seed of such a wave, in that it will initiate sticking very soon, after it reaches the bow following the first reflection off the bridge. The counterclockwise traveling kink is reinforced, in that if the bow is near the bridge, it slides by the string fast during the slipping, and slowly in the appropriate direction when it sticks—just what the doctor ordered. The clockwise kink is the opposite in this respect and is not reinforced, withering away due to friction with an uncooperative bow. — Eric J. Heller, Why You Hear What You Hear- An…, 1759

Categorization

Category: Causal Relationships

• DEFINE: Explains Helmholtz mode formation as a nonlinear cooperative resonance begun by one reinforced kink.

Related

• A self-reinforcing kink seeds the Helmholtz wave while its twin is damped away (similarity 0.96)
• The violin’s harmonics are phase-locked so their sum produces a traveling kink (similarity 0.86)
• Bow stick-slip generates a sawtooth Helmholtz wave with rich harmonics (similarity 0.83)
• Plucked strings vibrate as a sum of harmonic partials, not as a pure tone (similarity 0.81)
• A bowed string drives the bridge with a sawtooth waveform (similarity 0.80)
• A bowed string moves as a traveling kink, discovered by Helmholtz. (similarity 0.80)
• Bowing forces stiff-string partials into perfect harmonic alignment through phase-locked entrainment (similarity 0.78)
• Bowed strings alternate between stick and slip motion (similarity 0.78)