Vibrational Modes of Drums

Drums resonate in various ways, creating different vibrational patterns. A mathematical language has been developed to define the different resonant vibrational mode patterns in a circular membrane. The scheme involves counting the number of directions (0 means it goes in all directions) and the number of nodal rings.

(Number of Directions, Number of Rings)

Here are the most common drum modes. Click on the picture to see an animation of each mode.

Click the picture to see an animation.	(0,1) The first or the fundamental mode of vibration of a circular membrane is the (0,1) mode. This is the mode that is excited when the drum is struck in the center of the membrane. It sounds like a deep "thump." The vibrations occur at the lowest frequency of all of the drum vibrational modes.
Click the picture to see an animation.	(1,1) The second mode of vibration of a circular membrane is the (1,1) mode. This is the most important vibrational mode in terms of the musical quality of the drum. The (1,1) mode vibrates at a frequency 1.593 times the frequency of the (0,1) mode, and the nodal point runs the diameter of the drum.
Click the picture to see an animation.	(2,1) The third main mode of vibration of a circular membrane is the (2,1) mode. This is the second most important vibrational mode in terms of the musical quality of the drum. The (2,1) mode vibrates at a frequency 2.135 times the frequency of the (0,1) mode. The nodal point run the diameter of the drum at right angles to each other, making a large X.
Click the picture to see an animation.	(0,2) The (0,2) mode has one nodal diameter, or node in the form of a circle where the surface does not move. This mode vibrates at 2.295 times the frequency of the (0,1) mode and decays faster than the (1,1) mode, so it does not contribute to the musical quality of the drum, but to the thump.
Click the picture to see an animation.	(1,2) The (1,2) mode vibrates at 2.917 times the frequency of the (0,1) mode and does not contribute to the musical quality of a drum, even though it takes a relatively long time to decay.
Click the picture to see an animation.	(2,2) The (2,2) mode vibrates in a complex pattern that acts somewhat like two opposing 4 pole sound sources. It is the combination of one circular node intersecting two radial nodes which form a large X.
Click the picture to see an animation.	(0,3) The (0,3) mode has two circular nodal points and vibrates at 3.598 times the frequency of the (0,1) mode. The first nodal point is hard to see in this example but occurs near the center. This mode adds to the sound of the thump when the drum is struck in the middle, but not to the musical quality of the drum.