What does the little box do between the cat and muffler?

I replaced my muffler last night on my 1991 318i (OEM Eberspaecher) ($169). Sounds good.

I am curious though; what is the technical function of the small box between the catalytic converter and the muffler? I believe it is called a "resonator". Why is it there?

A resonater usually works in conjunction with the muffler to help reduce noise output from the exhaust. Where a muffler reduces noise over a wide frequency range, a resonater can be tuned for specific ranges, maybe one that the muffler isnt well suited for.

There can be some differences in the way they operate, but thats a small summary.

I wasnt aware the M42 needed a resonater. There isnt one on the M20.

13?

That's where the mice live ...

Yes.

No, that part is called the "seat cushion."

probably because the inline 6 runs a lot smoother than the inline 4, I know E36 318s get a little raspy sounding without the resonator

It is also because of the higer cruising revs the 4 cylinder cars. The higher the revs, the higher ther frequency of the pressure waves. Higher frequency pressure waves hit their peak annoyance in shorter lengths of pipe so a resonator is needed to keep that in check. The 6 cylinder cars don't normally cruise at the same revs as the 4 bangers.

Unless you are running 4:10 diffs!!! (Plural is correct, I've got an ix)

My wife's 318ti auto had a 4.44 diff! I left it on for a couple of days after I did the 6 cylinder/5 speed swap. Talk about high revving.