I like that photo above. When I was a kid that would have been a cool mom.
Here's an image of a bike with an expansion chamber with built in silencer. (it's from the expansion chamber thread) The silencer really brings down the exhaust note from sounding like a chain saw to sounding more like a quiet lawn mower. The silencer is the "tail pipe" of the chamber. (red colored tube under the seat)
Expansion chambers are different than mufflers as they effect the power of the motor and at what speed the power band occurs. Some expansion chambers don't have silencers and "clamp on" silencers are purchased and used on them. Motorcycle shops generally sell those. They are a larger piece of tubing that has a smaller tube in the center. It can be removed and fiber glass wool can be rolled over the core and then inserted into the silencer. That's secured with a clip at the end of the silencer which holds the core in place. Those with the built in silencers have similar.
But if you have someone who is handy with tubing and tools they could route a pipe upwards from the motor and route it like in the photo and use a small muffler the same way. (a muffler won't require a silencer)