Bow stick-slip cartoon

The bow on the right has some horizontal strips on it to show how the string and the bow move at the same speed while the string is "stuck" to the bow. The Helmholz kink travels around the string bouncing off the ends (and flipping sign) at a velocity proportional to the square of the tension in the string divided by the mass per unit length of the string -- the higher the tension the faster the kink moves. The larger the masses per unit length, the slower the velocity of the kink.

This movie is clearly a cartoon. No kinks in a real string can be as sharp as indicated here. Also it does not take into account damping-- either at the bridge where the string drives the vibration of the rest of the body of the instrument, or along the string itself, where internal friction in the string itself tends to damp out the sound, or even at the bow itself ( the slip is not frictionless and there is creep along the bow by the string even during the stick phase.)

at any point along the string in this model, the velocity of that piece of string is piecewise constant, with sudden transitions when the kink passes by.