Motorcycle exhausts seemingly play a very simple role, ferrying waste gas from the cylinder head to the outside air. But the difference they make to engine character and motorcycle performance is far greater than their basic, inert appearance suggests.
With a four-stroke engine, the exhaust valve opens and the rising piston pushes hot gas, crammed with residual combustion pressure and noise energy, into the exhaust system. This creates a positive pressure wave, traveling down the header pipe towards the collector. When it reaches the large diameter section (or another tailored change of section or shape) the gas expands, slowing down and sending a negative pressure wave back towards the cylinder at the speed of sound. This reflects back and forth around three or four times.
For a small amount of time when the exhaust valve is open, so is the inlet valve. This overlap. It's necessary in high revving engines – the valves need to be open a sufficient time to let useful amounts of gas past, and so exhaust closing gets later, inlet opening earlier, and the overlap period increases as the designer targets higher revs. This causes problems. Valve timing won't be ideal at low revs, and gar flow can be compromised – waste gas can get back into the combustion chamber, taking up space and getting in the way of the next combustion cycle. Volumetric efficiency and torque drop dramatical. An exhaust pipe's pressure waves are useful here. The length and diameter of the header pipes is set so the returning negative wave reaches the cylinder as overlap occurs, ensuring everything flows in the correct direction by effectively sucking the waste gas out and starting to flow fresh charge into the combustion chamber. A couple of milliseconds later, just as the exhaust valve is closing, it's useful for the pressure waves pin-balling around the exhaust to appear in positive form. This pressure wall prevents the fresh intake of mixture short-circuiting directly into the exhaust.
This is all wall and good, except the pressure waves in the exhaust move at uniform speed regardless of revs. Short header pipes might supply the negative/positive double-hit of pressure at the cylinder at the ideal time on a high revving engine, but won't be right at lower speed. An exhaust working well at 10,000rpm will also work, to a lesser degree, at 5,000rpm, in between – at t 7,500rpm – it'll be wrong. The pressure waves will be out of sync with the engine, spoiling efficiency and causing a dip in the torque curve.
For a race motorcycle this doesn't matter, most riders taking a few more horsepower at high revs in return for a few sacrifices. But it's a problem on the average road motorcycle, especially when silencing and exhaust emission rules causes further problems – any sudden restriction in the exhaust can reflect high pressure, making the engine work harder to pump waste gas out, sapping engine power. Therefore it's important that you select your aftermarket exhaust system with some care and check if the exhaust system you're looking at offers the right character to your motorcycle.