Circular Drum Head Modes: Understanding Why They Don't Always Follow the Rules

[RedX]

The modes of a circular drum head are described by Bessel functions and sines and cosines, but without getting into all that, one can making the following statement: the nodes are circles concentric with the center of the drum, and are also evenly spaced lines that run through the center of the drum (i.e., diameters).

However, while watching this video on youtube:



the first few modes are all right, but later on at higher frequencies, the modes don't seem to meet the description above. Why is that?

 

[Cleonis]

The modes of a circular drum head
[...]
the nodes are circles concentric with the center of the drum, and are also evenly spaced lines that run through the center of the drum (i.e., diameters). [...]
However, while watching this video on youtube:

I think that if you would be able to get a material with perfectly uniform mass per unit of area, and perfectly uniform elasticity, stretched with perfectly uniform tension, then - due to the conditions being perfectly uniform - the vibrational modes will be symmetrical. In the case of the latex sheet in the video I think all of the above factors are somewhat off.

I think it's a bonus that resonances are occurring at all, given the non-uniformities.

Cleonis

 

[Andy Resnick]

The modes of a circular drum head are described by Bessel functions and sines and cosines, but without getting into all that, one can making the following statement: the nodes are circles concentric with the center of the drum, and are also evenly spaced lines that run through the center of the drum (i.e., diameters).

However, while watching this video on youtube:



the first few modes are all right, but later on at higher frequencies, the modes don't seem to meet the description above. Why is that?

I vote that the tension on the head is not uniform. I wonder if you can tension the head (one lug at a time) while observing the patterns, and watch the pattern move.

Also surprising to me, the nodes are so low in frequency- that explains why the sounds of a struck drum are so disperse.

 

[RedX]

There are a lot of videos on youtube that show resonance patterns in various materials. There's even a name for it: cymatics.

One of the coolest ones I've seen makes life-like forms emerge:



There seem to be entire religions/philosophies built around sound frequencies and the resonance patterns that emerge from the boundary conditions.

But they're fun to watch.