Bows and strings

With high static friction, the bow tends to stick to the string ("stick" in the animation) and for a while it drags the string along with it. Meanwhile, the kink in the string travels along the string and reflects at the fixed end. When the kink returns to meet the contact point, the tension in the string now acts to pull it off the bow. Under appropriate bowing conditions (that are not easy to learn!), it breaks free of the bow and then slides past it easily with very little friction, thanks to the low kinetic friction. This is the "slip" phase in the animation.

The string doesn't stop when it gets to the straight position because its momentum carries it on until eventually it stops and reverses direction. Meanwhile, the kink has travelled to the near end of the string and reflected back. At the end of the "slip" phase, it is going at about the same speed and in the same direction as the bow. At this point, it catches on the bow again, static friction reigns, and the cycle begins again.

Usually the vibration of the string governs the cycle of stick-slip: while the vibration is in the same direction as the bow travel, it sticks and moves with it, when it reverses it slips. Thus the cycle of stick and slip on the bow has the same period as the vibration of the string. This might be less than a thousandth of a second for a violin or several hundredths of a second on a double bass.

Do not confuse this cycle with the forward and backward motion of the bow: while the player is moving the bow in one direction hundreds of stick-slip cycles may occur. (In the animation, only three cycles of stick-slip motion are shown, to keep the file size acceptable.

Further, it is only an up-bow. When the bow reverses direction, there is inevitably a small but usually noticeable discontinuity in the wave motion, which is a key element of articulation for string instruments.

The bow allows the player to put energy into the vibrating string and to play long sustained notes. It also allows a range of different transient effects and articulations. The bow string interaction is important in less obvious ways, too. Over a limited range of force applied by the player (players call this "pressure"), the cycle of stick and slip is governed by the standing wave in the string.

When this happens the motion of the string is nearly exactly periodic, and it therefore makes a sound with an almost exactly harmonic spectrum. This means that any inharmonic effects of the string are reduced by bowing, which is not the case when the string is plucked. The periodic motion of the string includes rather sudden changes in direction, and these imply substantial power in the high harmonics. The regular action of the stick-slip action thus puts power into the high harmonics and contributes to the richness, brightness and loudness of the violin's sound.

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