If you want to understand just how much the exhaust system does, try driving a vehicle with bits of it missing...
The abovementioned mechanic did LPG conversions and sometimes there would be a need to alter the path of the exhaust system to get around the LPG tank. I was the one usually chosen to drive these vehicles over to the exhaust place - and let me tell you, you get a REALLY good first hand lesson in the accoustic output of even the most moderate engine - especially when under load. As a result, my driving in these situations was extremely conservative - but there was still a bridge over a railway that had a steep approach and the noise was intense.
Sometimes the only bits of the exhaust still attached were the manifold, engine pipe and catalytic converter. BIG noise! (and, yes, I was constantly looking in all directions for any police interest - which I never encountered, thankfully)
Had my exhaust replaced recently, had to limp around town with nothing on while they were getting parts in. Even the weedy engine in my Toyota sounds like a hotrod* when it's loud and open like that.
*A hotrodded lawnmower, to be more honest / accurate.
Also quite a difference; the previous system I had, was welded from pipes and parts. In particular it was missing a mid-line resonator. Never quite sounded right. (This time around, it's all aftermarket or OEM parts, close enough to original. Sounds about right.)
Also a little surprising how much, and how little, difference can be made from little leaks here or there. Rusted out pipes tend to get loud, and add a rougher sound with more hiss (modulated hiss -- turbulence on the pulses). Sound from underneath or behind the vehicle tends to carry pretty well. OTOH, leaks in the engine bay don't seem to do much, presumably as the sound is forward-facing and reasonably well absorbed and scattered by everything in there. (They weren't able to seat the downpipe quite right so I had this going on, before getting it re-checked.)
Tim
My 1999 Toyota Camry sounds like an antique "sewing machine" externally at start up.
I can usually recognise Toyotas from around that year, as they all sound like that.
Strangely, my Camry sounds beautifully smooth & nearly silent when cruising on the open road.
My old Leyland P76 V8, with an after market twin system sounded great --- classic "tuddy, tuddy" sound when cruising the back blocks of the WA wheat belt.
The kids loved it--- they would sit in the back, with the windows down, revelling in the sound, & the air rushing in.
They liked to get in & out through the windows, "Dukes of Hazzard" style!
When I was a kid, I particularly liked the old "sidevalve" Ford Customline exhaust sound, too.
The sound that really gets my attention, however, is a big old turbocharged Dorman Diesel firing up.
When this happened, it was when a power fail occurred, so there is an element of "Pavlov"s dogs" in it!
The next place I worked had Detroit Diesel Standby plant, much more efficient, but for character, they never quite matched those scary old "Brit beasts"!