That would have to do with how tightly it's stretched. the tighter the higher the frequency. Think of how a guitar string vibrates. Maybe it would need some experiments with latex glove, trash bag material or?

But he is trying to emulate the water in a rippling in swimming pool (maybe 1 to several Hz, I would guess) with a device maybe 2 inches in diameter. Don’t see it happening.

Added video:

 

Here is where I am at with this. I found a 4 pack of solenoids on amazon for about $8 with a 4mm throw. I am going to mount the three LED bulbs (each with a multitude of blue, white and green LEDs and individual controllers each to cycle through the colors) on a piece of spring steel wire. each of the three wires will come together and mount into a washer. The solenoid will mount below that washer and control a rod that goes up through the washer and connect to something (thinking plastic bead from mardi gras) a little larger than the diameter of the washer so when the solenoid is thrown, the wires will come together and when off, it will push them apart. I can change the frequency of the movement with the length of the spring steel wire. So I should be able to create a pretty good random/natural pattern combined with the controllers on each of the LEDs. I will post pics of each iteration once I get a chance to actually build it (work is crazy right now) as well as video of the result if you guys are interested.

Thanks again for all of your input. It helped enormously!