What makes a loud exhaust loud?

[BACI]

I’ve always thought that the sound of the fuel-air mix igniting in the engine cylinders was the cause of the noise I heard through the exhaust system of a vehicle. Indeed, take off the exhaust altogether and a small engine can sound overwhelmingly loud.

Then it occurred to me that in a four stroke engine, the exhaust stroke comes after the ignition stroke, and that the explosion within the cylinder will have well and truly concluded prior to the exhaust valve opening up and releasing whatever was in the cylinder into the environment.

So if the bang has already happened by the time the exhaust system comes into play, why do modified exhausts make a vehicle sound louder?

[beowulff]

There’s still plenty of pressure in the cylinder at the time the exhaust valve opens:

Near BDC, the exhaust valve opens, releasing any cylinder pressure which is higher than atmospheric pressure. This is called “blow down”. Depending on the cylinder pressure and how quickly the valve opens, a loud or sonic pulse can be generated. That is where the exhaust noise comes from, and why engines make more noise at full power than at idle.

Here is a graph.
Looks like 100psi.