There are two types of "wave" occurring in a 2 stroke engine exhaust.
The first is a pressure wave caused by the "slug" of exhaust gas entering the exhaust pipe. This gas has inertia and tends to keep on going. Behind it tends to occur a low pressure.
The second "wave" is a shock wave (positive pressure) caused by the sudden opening of the exhaust port. This wave doesn't have inertia and can easily be reflected. As the wave travels outwards and leaves the pipe end, a negative pressure reflection occurs at the outer end of the pipe.
The skill of tuning these engines for absolute maximum power comes from the shape and length of the pipe and as already been mentioned, from the shape and "timing" of the ports. Timing the ports is achieved by their position in height on the side of the cylinder. Getting these two just right can cause a double negative wave to "suck" the remaining exhaust gases out of the cylinder and allow a very full or even "supercharged" fresh charge of mixture to enter the cylinder.
A characteristic of 2 strokes is that they tend to have quite a narrow power band. A particular exhaust may work brilliantly at one engine speed but not at all well at lower or higher RPMs. "Coming on the pipe" can be likened to a musical wind instrument player suddenly hitting the perfect note. The intake reed valve mentioned earlier is actually quite a recent innovation, as are ancilliary systems which vary intake and exhaust characteristics to make an engine more flexible and economical with low emissions. It was the difficulty of keeping emissions low enough to comply with modern legislation that almost killed the 2 stroke motorcycle industry over the past few years. The fresh charge tends to mix with the previous stroke's exhaust gases.
Some older motorcycle engines would run backwards if the ignition timing was incorrectly set, very interesting for the rider and highly amusing for onlookers!
The next logical step is 2 stroke direct injected diesels. They can give the best of the 2 stroke petrol engine (high power and light weight) with the economy of a diesel engine but only pump air on the induction stroke so the emissions can be much more strictly controlled. I am certain we are going to see a lot of cars (and hopefully aircraft too) running these engines in the next few years. Diesels of course don't suffer from carb icing - there isn't one - and they don't require vapourisation of the fuel in the manifold.
Last week I ported up my son's R/C car glowpug engine for him. The increase in power is amazing; so much so that the car will wheelie and flip completely over backwards if given full throttle too quickly. The downside is that he's told me it is now illegal for the class of racing that he was going to run it in!