Question

When the stick strikes the drumhead the contact produces a large, brief normal force: the drumhead pushes on the stick and the stick pushes equally and oppositely on the drum (Newton’s third law).

Answer 1

Yes — that’s exactly right. When the stick contacts the drumhead the interaction produces a short, large normal force pair: the drumhead pushes the stick and the stick pushes the drumhead with equal magnitude and opposite direction (Newton’s third law). A few useful consequences and clarifications:

- These two forces act on different objects, so they do not cancel each other out; they change the motions of the stick and of the drumhead independently.
- Because the contact is brief, the force is usually treated as an impulse. The impulse J = ∫F dt equals the change in momentum Δp of each object (stick and drumhead, with opposite signs).
- The drumhead’s response (displacement, vibration modes, and subsequent sound radiation) depends on its tension, mass distribution, boundary conditions, and damping. The stick’s rebound depends on its speed, the hand’s constraint, and the collision’s effective elasticity.
- Energy considerations: some kinetic energy of the stick is transferred to the drumhead (and then into sound and heat); some may be returned to the stick if the collision is elastic, or lost if it’s inelastic.
- Real collisions are affected by contact time, material stiffness, damping, and the geometry of impact, which determine the force profile, the stick’s rebound, and the timbre of the drum.

If you want, I can show the impulse calculation for a simple model or discuss how head tension changes the sound.