A self-reinforcing kink seeds the Helmholtz wave while its twin is damped away

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. … 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