When the kink is between the bow and the fingered end of the string, the string moves at the same speed and in the same direction as the bow. Only a small force is needed to lock the two motions together. This is known as the "sticking regime" (figure 2a). But as soon as the kink moves past the bow - on its way to the bridge and back - the string slips past the bow and starts moving in the opposite direction to it. This is known as the "slipping regime"
Although the sliding friction is relatively small in the slipping regime, energy is continuously transferred from the strings to the vibrational modes of the instrument at the bridge. Each time the kink reflects back from the bridge and passes underneath the bow, the bow has to replace the lost energy. It therefore exerts a short impulse on the string so that it moves again at the same velocity as the bow.
This process is known as the "slip-stick" mechanism of string excitation and relies on the fact that sliding friction is much smaller than sticking friction (figure 2c). The Helmholtz wave generates a transverse force Tsinq on the bridge, where q is the angle of the string at the bridge. This force increases linearly with time, but its amplitude reverses suddenly each time the kink is reflected at the bridge, producing a sawtooth waveform . The detailed physics of the way a bow excites a string has been extensively studied by Michael McIntyre and Jim Woodhouse at Cambridge University, who have made a number of important theoretical and experimental contributions to violin acoustics in recent years.
It is important to recognize that the Helmholtz wave is a free mode of vibration of the string. The player has to apply just the right amount of pressure to excite and maintain the waveform without destroying it. The lack of such skill is one of the main reasons why the sound produced by a beginner is so excruciating. Conversely, the intensity, quality and subtlety of sound produced by great violinists is mainly due to the fact that they can control the Helmholtz waveform with the bow. The quality of sound produced by any violin therefore depends as much on the bowing skill of the violinist as on the physical properties. One of the reasons that the great Cremonese violins sound so wonderful is because we hear them played by the world's greatest players!
