Consider an open disk of radius centered at the origin, which will represent the "still" drum head shape. At any time the height of the drum head shape at a point in measured from the "still" drum head shape will be denoted by which can take both positive and negative values. Let denote the boundary of that is, the circle of radius centered at the origin, which represents the rigid frame to which the drum head is attached.
The mathematical equation that governs the vibration of the drum head is the wave equation with zero boundary conditions,