I just learned in the context of a PDE course how the various modes of vibration arise as solutions to the 2D Wave Equation. I am curious as to how many of these describe the motion of actual drums.
Clearly the size and shape of the drum matter as far as the mathematical solutions are concerned. However, I would expect some qualitative invariance, for example, that the modes of one circular drum would be a scaled version of the modes of another circular drum of a different size. Can a single, circular drum be made to vibrate in any of the modes shown at the above link, depending on "performance" factors such as the location where the drum is struck or the ambient conditions, or is the vibration behavior restricted by external factors such as the type/material composition of the drum?
Also, I am assuming from the fact that there was a debate on whether or not the shape of a drum can be heard that the actual audible difference between the various modes is not immediately obvious. Is this assumption correct? Is the difference in sound extremely subtle, or do producers manipulate the various vibration mode behaviors when synthesizing drums to create unique sounds?