Some design considerations - your plan will be customised to your bike, but in general you'll need three parts.
Batteries Depending on budget, you may end up having to use some car batteries. That would be the older way of powering your rig, but they've heavy and relatively fragile. More modern batteries would be smaller and lighter but cost more.
You'll also need some way to charge them safely beforehand.
There are modern "powerbanks" that can provide USB levels of voltage at 5V or some that will provide 12V, which might be ideal.
Sound source You might want to use a phone via a wire or bluetooth, but a dedicated source would be better. Imagine getting a phone call while the music is playing.
A 12V device is perfect, because 12V batteries are common. And a common 12V sound source is a car stereo. A modern car stereo can play MP3 from a SD card or USB drive. And if there's no tape or CD mechanism then they're really quite shallow depth, which helps with your physical build. You can wire a car stereo straight to your 12V battery with nothing more than wire and joiners.
Downside, car stereos are not particularly waterproof, so you would want to put it under some sort of cover.
Speakers Gotta get the sound out somehow, and speakers (more accurately Drivers/cones) are the only way to do that. You could salvage speakers from an old hifi speaker cabinet. This has the added advantage of providing big and small speakers plus whatever crossover circuit is in the cabinet.
If cost isn't an issue, then "outdoor-rated patio speakers" would be a good choice.
Enclosure This is where it gets hard. You want some kind of way to mount your stuff on your bike so it can still be ridden, but also to support and protect the components. Generally speaker boxes are made from reasonably thick plywood/customwood/chipboard. And you don't want to add silly amounts of wood to your bike.
So work on paper and see where you need to leave clear for your legs and arms, and clearance areas for turning. Upshot - there's some space in the main triangle, but the larger areas are on a rear rack and over a front rack. That would be an excellent starting point.
Do make sure your stuff isn't loose - it must not fall off at any point for any reason. Use saddle clamps screwed into the wood, and not cable ties or bungees or springs.
- Combine 3 and 4 by simply reusing some old speaker boxes from a defunct stereo, and strapping them over your rear rack.
This might be getting a bit too much - look at that poor rear tyre, and that they've had to weld on outrigger wheels.
Other considerations for you to be aware of
- Copyright and rebroadcasting - Music isn't free. The music you might hear on the radio is paid for on a per-play basis to the copyright holder. Its conceivable that you might get asked for your "rebroadcasting licence"
- Being antisocial - Critical Mass gets a bad reputation sometimes for being a disturbance. Consider that you want to avoid a Noise Control or "Breach of the Peace" notice.
- Fellow Riders - Riders next to you don't want to be deafened - Be aware of the maximum sound output of your rig.
- Waterproofness and crashworthyness. Bikes get bumped about, and sometimes its not fine and sunny. Consider what needs to be dry or protected.
- Taste - There could be families with kids on the ride, so consider the lyrics and appropriateness. Sing-a-long type songs might be a bigger hit than "judas megaslaughter" Use good judgement - perhaps even have a set of USB drives with different genres/playlists pre-prepared.
- Don't bother with stereo - sound quality and imaging is not going to happen. So use mono only.