## The Bow-String Interaction

• An approximation to the friction force exerted by the bow on the string is shown in Fig. 4 (Keller, 1953; Friedlander, 1953). The curve is antisymmetric because bowing can happen in two opposite directions. This force is dependent on , the difference between the bow and string velocities.

• The bow and string are stuck together for (the point of infinite slope in the figure). In this case, the friction force is based primarily on static friction.

• For , the string is slipping'' and the friction force is based roughly on kinetic friction, which is significantly less than the static friction (especially when rosin is applied to the bow).

• The maximum friction force is roughly proportional to the normal force between the bow and string.

• At all times, the force applied by the bow on the string must balance the reactive force of the string.

• The reactive force can be expressed in terms of the string wave impedance and traveling-wave components of velocity as fs = Rs [vs+ - vs-] = Rs [vs - 2vs-], where Rs is the string wave impedance.

• A graphical solution can be found by plotting this expression together with the friction force expression to determine a resulting outgoing traveling-wave component, as shown in Fig. 5.

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