In Search of the Missing Fundamental: by Richard K. Jones
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Membrane Modes

The (0,2) mode
The fourth mode (0,2), shown below does not have any diameter nodes, but has two circular nodes – one at the outside edge and one at a distance of 0.436 a (a is the radius of the circular membrane) from the outer edge. The frequency of the (0,2) mode is 2.295 times the frequency of the (0,1) mode. Like the (0,1) mode, the (0,2) mode is excited when the membrane is struck at the center. The sound radiation characteristics of the (0,2) mode are more complicated than the first three modes — it appears to be a mix between a monopole and a dipole. Its decay time is longer than the (0,1) mode, but shorter than the (1,1) mode. As a result, it contributes to the thump sound when a drum is hit at the center, but does not contribute much to the musical pitch of a drum when hit off-center.


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