Slippery finger pushing on a large drum head.

[Spinnor]

Say I push down on a very large drum head that lies in the z = 0 plane at equilibrium. Suppose there is no friction between my finger and the drum head. Suppose my finger tip pushes the drum head down some distance d. Suppose I accelerate my finger tip to some constant velocity v in the x direction while always keeping my finger tip in the plane z = -d.

Are waves produced during the acceleration of my finger?

Once my finger is in motion does it tend to stay in constant motion, that is does the drum head resist acceleration or deceleration of my finger tip?

I hope this is the right forum. Thanks for any help!

 

[kenif]

Concentric waves will form in the drumhead, the nature of the wave being a result of the excitation velocity, the drumhead material and fluid (presumably air). The result is that the wave will transfer energy to the fluid where frequency is a function of wave diameter. In other words, higher frequencies will come from the area closest to the finger, and lower frequencies towards the perimeter. These waves are further modified by the drum enclosure and the immediate environment. Drum waveforms are surprisingly complex.

This radial variation characteristic is used is full-range loudspeakers and sometimes called a "mechanical crossover". Full-range speakers tend to be either very crummy or fabulously expensive audiophile units.

The drum head would resist acceleration, at higher velocities most work would be done by the fluid.