When you bow a violin string, the string vibrates at a specific frequency. It sounds louder when you bow faster - that is when the string stick and slip against the bow with larger displacement (or amplitude). Vice versa, smaller amplitude or a slower bow yields a softer sound. That is how it is explained.
The part that I don't get is how bowing faster increases the amplitude and makes the sound louder. The bow pulls the string by friction. Friction decreases as velocity increases, and static friction is bigger than dynamic friction. If I bow really, really slow to model the force between the bow and the string as static friction, this static friction should pull the string further away and result in a higher amplitude. Now if I bow really fast, the force from this dynamic friction should be smaller than that in the static friction produced by slow bowing, hence pulling the string with smaller amplitude instead.
Thinking in terms of frictional force, bowing faster should give a softer sound - which of course is not the case. Could someone help explain or correct the concept or physics behind it?