Question regarding Muffler to silence exhaust noise

OK, I just got a really good exhaust fan, rated at 200 CFM, which is about twice what my space requires even when calculating the carbon filter, and other drag on the system. I bought a fan that was too big because I was going to use a speed controller with it. Well the speed controller I got will not control the fan, when I use it, it emits a loud hum, and will not turn the fan on unless I turn it up to full power. Which is way too loud for what I want. I am naive and thought that you could run any fan with a speed controller, turns out you can't. The fan I have is apparently a capacitor start motor which is not speed controllable. So unless I purchase a new fan that is useable with a controller, I need to find a way to quiet this one.

I am considering either making or purchasing a muffler to help quiet down the noise. Most of the noise is from the moving air. So I think this might be a very effective way of dealing with the problem.

My question is where in the chain do I put the muffler. I run a carbon filter, that has to be at the end of the chain, as it is not an inline filter. So with the filter at the end of the run, should I put the muffler at the beginning, right after the fan?

Fan > Muffler > Duct work > Filter

Or should I put it right before the filter? I think the filter acts as a bit of a muffler anyway.

So what are your thoughts on this?

Also if anyone knows of an easy way to control the speed of a capacitor start fan, one that won't burn out the fan, I would like to know that too.

Thank you.

You should put the fan closest to the filter so that you dont lose air pressure and keep the fan from overworking itself.

Filter > Fan> Ducting > Muffler

I also have heard of people using light dimmers to use as fan speed controllers, cost effective!

Thanks for the information. So you are saying that I should pull air into the filter, then out the room, rather than pull the air out of the room then push it into the filter? I guess I had it backwards. Thanks.

one more thing, if I hook it up like this:
Filter > Fan > Ducting > Muffler
Will I still be able to exhaust enough air to cool the room
Right now I don't have a muffler but I have it set up like this:
Fan > Ducting > Filter
This works fairly well at controlling the temp. Would putting the filter first still allow the fan to pull the heat out of the room? The fan is about twice the size I need based on formulas I have found here.

Any thoughts?

Thank you.

The temp will be fine if it wasn't an issue before.

Try putting your fan in a cardboard box with a load of insulation, it cuts down on sound hugely.
(Edit) As well as I meant!