Vibrations Of A Circular Drum
The vibrations of an idealized circular drum head—essentially an elastic membrane of uniform thickness attached to a rigid circular frame—are solutions of the wave equation with zero boundary conditions.
There exist infinitely many ways in which a drum head can vibrate, depending on the shape of the drum head at some initial time and the rate of change of the shape of the drum head at the initial time. Using separation of variables, it is possible to find a collection of "simple" vibration modes, and it can be proved that any arbitrarily complex vibration of a drum head can be decomposed as a series of the simpler vibrations (analogous to the Fourier series).
Read more about Vibrations Of A Circular Drum: Motivation, The Problem, The Radially Symmetric Case, The General Case, Animations of Several Vibration Modes, See Also
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“Out of me unworthy and unknown
The vibrations of deathless music;”
—Edgar Lee Masters (1869–1950)
“The world is never quiet, even its silence eternally resounds with the same notes, in vibrations which escape our ears. As for those that we perceive, they carry sounds to us, occasionally a chord, never a melody.”
—Albert Camus (1913–1960)
“Whoso desireth to know what will be hereafter, let him think of what is past, for the world hath ever been in a circular revolution; whatsoever is now, was heretofore; and things past or present, are no other than such as shall be again: Redit orbis in orbem.”
—Sir Walter Raleigh (1552–1618)
“Not a drum was heard, not a funeral note,
As his corse to the rampart we hurried;”
—Charles Wolfe (1791–1823)