Understanding exhaust design begins with the basic appreciation of the behaviour of sonic waves travelling through a pipe. These waves travel at a speed determined by the temperature and pressure of out flowing gas. This speed always equals the speed of sound, which averages about 1675 feet per second in hot exhaust gas.

Sonic waves have the strange property of being reflected back along the pipe they are travelling through, regardless of whether the pipe has an open or closed end. Even more peculiar is another fundamental law of acoustics that causes a pressure wave to invert its sign upon reaching the open end of a pipe. A positive wave, on reaching the pipe's end goes back up the pipe as a negative wave, and vice versa. Reflection from a pipe's closed end does not change its sign, a positive wave stays positive.

The earliest exhausts were a piece of straight pipe, but these were not able to take full advantage of pulse waves to suck exhaust gases out of the cylinder. In this type of system a positive pressure wave charged down the pipe immediately as the exhaust port opened. On reaching the end of the pipe, it was reflected back as a negative wave but with reduced intensity, because much of its wave energy was lost to the surrounding atmosphere. However, some energy did remain, and if, when the negative wave reached the exhaust port, the port were still open, it would assist in a small way in evacuating the cylinder. This being the case, the wave would turn around and travel back down the exhaust still negative, then, upon reaching the open end of the pipe, be reflected back up as a positive pressure wave. If the exhaust was of correct length, the positive wave should have arrived back at the exhaust port just before it closed, forcing any fuel/air mixture that had spilled into the exhaust back into the cylinder to be burned.

In theory, it sounded good, but in practice the straight pipe didn't work well. This was true primarily because so much kinetic energy was lost each time the sonic wave reached the open end of the exhaust pipe. A two-stroke requires strong pressure pulses to work efficiently, so engineers added a megaphone to the end of the straight pipe.

A megaphone, more correctly called a diffuser, is in effect a relatively efficient energy inverter. In a diffuser, the diverging walls cause the sonic wave to react just as if it had reached the open end of the exhaust. However, the reflected wave retains most of its energy and can create a vacuum as high as 6 psi. Obviously, a pulse wave of this magnitude can be very effective in drawing exhaust gas out of the cylinder and in pulling the fresh charge from the crankcase up through the transfer ports.

The problem with this system is that much of the time the strong negative pulse wave will arrive at the wrong moment and draw a considerable amount of fuel/air mixture into the exhaust. The exhaust port will close before the reflected, positive wave arrives to force the mixture back into the cylinder.

The next step was to add a reverse cone with a small outlet to the diffuser. This proved to be the real breakthrough in two-stroke exhaust design. This type of exhaust is referred to as an expansion chamber. The addition of the reverse cone with a small bleed off hole acts as a closed pipe, giving the exhaust a double pulse action. When the positive wave reaches the diffuser, part of the wave is inverted and reflected back as a negative wave to evacuate the cylinder. However, part of this wave continues to be reflected by the reverse cone. Because of the pressure build up caused by the small bleed hole, the reverse cone acts like a closed pipe, reflecting the wave with the same positive sign. This strong positive pulse arrives just before the exhaust port closes, forcing any escaped mixture back into the cylinder, increasing power output and reducing fuel consumption.

The Belly section of the pipe determines the relative timing of the negative and positive waves. The exhaust timing, transfer timing and shape of the power curve required will determine the length of the belly section. A longer belly section will bring the torque and horsepower peaks closer which tends to increase top end horsepower. A shorter belly will spread the torque and power peaks, which has the effect of broadening the engines power curve. The belly diameter is determined by the outlet diameter of the diffuser cone and has no direct effect on power characteristics. However, remember the angle of the diffuser and reverse cone does. Today's diffuser cones are usually a multi-angled affair, and the steeper the angle, the more intense the wave will be, the more the pipe can push and pull and the larger the outlet will be.

The stinger section of the pipe is a pressure bleed valve to allow the exhaust gases to eventually leave the pipe. Increased pressure in the pipe caused by a longer and/or smaller diameter stinger helps the wave action of the pipe and can increase performance of the tuned pipe. This is due to the high pressure creating a denser medium. Sound waves travel better in a denser medium. However, the more you restrict the stinger the higher the heat retained. This can be a very detrimental characteristic of a two-stroke engine, but the gains from a smaller stinger can yield considerable power increases. In many cases the stinger size will be tailored to the type of racing the motor will be used for.

This has been a simplified description of how a tuned pipe came to be. Today's tuned pipes use gradually tapered header pipes to keep gas velocity high near the exhaust port. Multi-angled diffuser cones help exhaust gasses expand and cool more gently and dual stage reverse cones add more volume to the pipe, which tends to increase midrange power.

Pipe design today usually starts on the computer followed by extensive dyno and field-testing. These peculiarly shaped exhaust pipes are largely responsible for the amazing power the two stroke engine is capable today.