Perhaps nothing is as prevalent in the powersports industry as the notion that aftermarket exhausts boost the power of any given four-stroke street bike motorcycle. Problem is, it ain't necessarily so. Let's look at this from all sides.
The Four-Stroke Engine
An internal combustion piston engine has pulses resonating in and around it, pulses that have nearly as much influence over engine efficiency as do the obviously mechanical actions of the cams, valves, intake tract, ignition, etc. To illustrate the truth of this, consider that no four-stroke engine manufactured in the past 70 years or more opens and closes its valves exactly at the beginning and ends of its piston strokes. This is precisely because of engines' inherent resonances and pressures, energies that play a huge role in cylinder filling and evacuation, to the point that they work in concert with the camshaft for example, a part that is actually designed with the assistance of these resonances in mind. Intake valves open quite a ways *before* TDC, because even with the piston still rising, cylinder pressures exist that assist cylinder filling, making it advantageous to make use of them and not rely on the valve's function alone. The same with the exhaust valve, which closes quite a ways *after* TDC because these same energies within the cylinder allow continued exhaust exit despite the now downward moving piston. These are simply a part of the nature of the four-stroke engine, and at work in the two-stroke as well (though of course they have a different kind of valve).
Acoustic Wave Theory
Two acoustic principles govern the ability of an exhaust system to improve the four-stroke engine's power through manipulation of these inherent pulses. The first is the principle of wave return. A sound wave will, upon reaching the end of a tube (the exhaust pipe), create a return wave that travels back up the tube. That's number one. The second is the principle of conversion. This returning pulse will be inverted if nothing about the pipe even partially restricts the original outgoing wave, or averted (i.e. not inverted) at the precise point the wave *does* encounter a restriction. So return and conversion, two principles. The way these two principles work in an exhaust system is this. An exhaust is a tube with both of these things in place -- an opening at the far end which allows wave expansion, and a cylinder at the other end which does not permit expansion. Thus return is of course at play, as are also both kinds of conversion: inversion and aversion, in any exhaust. These waves expand and invert at the atmospheric end, and do not expand and thus do not invert at the cylinder end. But they always return, and in fact the returning is contnuous, though eventually weakens, so we tend to count just the first four incidences or waves, and discount the 10th, 11th, and others So the action is: wave out, returns to the engine, returns to atmosphere, and returns to the engine again.
What Happens Inside the Engine
Okay, so that's the mechanics. But how does this affect the engine? Well, should the return wave (the second wave) arrive back at the cylinder at the right time, its negative pressure (because it is remember, inverted, because it encountered no restriction on the first trip) will encourage exhaust scavenging (enhanced exhaust gas evacuation) and at the same time added intake filling (due both to scavenging and to lower cylinder pressure), with the end result more air/fuel mixture in the cylinder. This wave then bounces off the cylinder wall to create a third wave. And since this return is against an enclosed space this third wave is *not* inverted but averted, meaning it goes back down the exhaust still a negative wave. Upon reaching the open expanse at the end of the pipe, it does what? Invert, of course, because remember a wave reaching an expanded area inverts when it returns, so the fourth wave then returns back up the pipe, now positive because of inversion, to arrive at the cylinder to put a halt to the scavenging effect started by the second wave. In other words it prevents *overscavenging* and fuel escaping into the exhaust system.
Does this stuff really work this way? Yes. Under certain perfect conditions, it works exactly as described. Wave two scavenges and wave four turns off scavenging, while waves one and three make two and four work. Resonance tuning is so powerful some engineers have actually called it "the third valve" (in addition to the intake and exhaust valves, of course).
And this is just the beginning. Because where tuning comes in, is, this stuff can be controlled by taking extra care in the design of the lengths and angles produced in the exhaust pipe. The exhaust's lengths control the timing of the return waves to the cylinder (waves two and four), while angles in the exhaust determine how strongly, i.e. with what force, they return and also their duration (strength and duration are opposites -- more of one means less of the other). For example, a very short pipe returns its waves faster, which suits high rpm power because the speed of the wave in the exhaust is constant yet things happen faster in the engine at higher rpm. Conversely, a longer exhaust pipe suits low rpm power better beause the delayed arrival of the return waves work better when the engine is doing everything slower. Make sense?
Ever hear of a reverse cone megaphone? It's a real thing that uses this same principle. The flip up at the back of an exhaust cone creates a companion return wave that returns at the almost the same time, but actually slightly behind, as the second and fourth waves, to lengthen the duration of their return effect, thereby broadening the powerband.
Now, there are naturally some qualifications to all this working. One, the exhaust's wave speed is constant while engine speeds are anything but. So the effect of any tuned exhaust is limited to a fairly narrow rpm range. In other words it can be tuned for low rpm, midrange, or high rpm, but not a combination. This can be overcome somewhat with the right angles and especially by use of the reverse cone (and lately by Nascar developed technology known as a resonator, simply a bulge in the headpipe), but all in all a tuned exhaust is tuned to a specific rpm zone. Second, there can't be any baffling inside the exhaust anywhere, as that would work the same as an area change, i.e. a restriction to the wave, and thus interfere with tuning. There are even problems with how heavy a gauge sheet metal the cones are made from, whether they're welded or brazed, and just exactly how they are bolted to the bike. All can affect how resonance works.
But the most important consideration of all, and the point when it comes to production motorcycles (as if the baffling issue wasn't a deal-breaker all by itself where road bikes are concerned) is valve overlap. Valve overlap was introduced above in the first paragraph, but you may have overlooked it. It is simply that spread of time around the center of the engine's operation, TDC to be exact, during which both the intake and the exhaust valves are open at the same time. All four-stroke engines have *some* overlap because as explained all engines open their valves earlier than TDC and close them later than TDC. Thus overlap. The thing is, overlap is the gateway to exhaust tuning. After all, you have to have the intake valve open if you want the returning wave to do anything. Same with the exhaust, naturally, as it is the entry point. But here is the catch. Because of emissions, during the final dozen years of the carbureted engine's last stand, valve overlap was shrunk until it hardly existed. The upshot is, even if you managed to find or build a tuned exhaust for your 1982 CB750, to *that* engine it will not be tuned, because that engine does not hold its valves open long enough for any of the stuff talked about above to work! That's right. Whether that exhaust improves engine performance or not (and this is itself pretty questionable), it does not do it by traditional, performance exhaust tuning, i.e. resonance wave effect tuning.
So how do aftermarket exhausts that improve power do so on production motorcycles? On vintage bikes? Weight savings, for one. Back pressure reduction, for another, but then we're talking a lot of noise. But notice I said "vintage.". Since the advent of fuel injection and other engine electronics, valve overlap has been on the increase again in modern engines. It may never in production emissions controlled engines be enough to completely expose the engine to all that the tuned exhaust can do (as happens in two-strokes), but it is more now than it was 15 years ago. And this is the primary reason exhausts made for old bikes do almost nothing or very little while exhausts made for ZX-14Rs do a lot. :-)
How can the exhaust companies sell stuff that doesn't work? I don't know what message the general vintage-owning public is getting, but on the inside of the industry it is well known that most of this stuff is useless. Denis Manning, Land Speed record-holder and owner of Bub exhausts many years ago told me a test bike they had on a dyno fell off and dented the exhaust, and on the next run the bike made more power! In other words, the aftermarket exhaust industry is hugely serendipitous! Unashamedly so! Terry Vance, another longtime racer and the name on many exhausts made and sold in the 1980s, once told a magazine that his company, Vance and Hines, knew they weren't selling performance, just bragging rights. The look, in other words, the sound. Yup. Exhaust fashion, like Vuarnet sunglasses. Read more on this subject here.