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That pipe looks like PVC, not polyethylene. Are you sure? Usually polyethylene is thinner and flexible, not thick and rigid.
I'm a little confused about when and how you would do this. You start out by saying many people don't have a monitor they can hook up to their RPi so they can use this instead, but the very first step is to hook the RPi up to a monitor. So you do in fact need a monitor that will work with the RPi in order to do this. Am I missing something?
You don't say what you want to control these lights with, but that's a lot of lights to individually control. However, you don't need a microprocessor to do it. There's a kind of chip called a "decade counter" that sequences through 10 outputs being high one after another. But they also have the ability to daisy chain these chips so when one chip has put it's last output high, it can signal the next chip to put its first output high. If you connect 10 of them then you can sequence all 100 pairs of lights.For an example circuit using the most common one, the 4017, see http://www.allaboutcircuits.com/textbook/experiments/chpt-7/led-sequencer/
Could you be more specific than "Sound module"? That's not very helpful. And is that a solid state relay or mechanical?
Arduino Frequency Detection
RainBoard - RGB LED Rainbow Fader