OK, I wasn't planning on doing this, but I'm going to have to present things as I would back in the fifties and then we'll try and work out a translation.
For calculations, I used a K&E Log-Log Duplex Decitrig slide rule. Many years later, I'd get a self assembly electronic pocket calculator from Great Britain. Chrysler's Engineering Center in Highland Park had an early IBM tube type computer (I've forgotten the IBM designation). In some ways, the computer was pretty crude. I mispunched a card and the computer was down for a couple of days. It was often more convenient to use a Friden to make vehicle performance calculations.
Anyway, here's how we visualized the workings of a tuned intake manifold. Valve closures and openings are assumed instantaneous. At the instant of valve closure, the intake runner is at zero pressure and the flow is toward the valve. The air (actually, a F/A mixture) impinging on the closed valve immediately rises in pressure to a value equal to ρVc or, in other words, the product of the specific density, the flow velocity, and the speed of sound.
So, this very small volume of high pressure air immediately begins to expand toward the open end of the runner, or, in other words, away from the closed valve. There exists, then, a zero thickness boundary (that which I call a front) moving away from the closed valve. Behind the front, the air is stagnant and at a high pressure. Ahead of the front, the pressure is zero and the air is flowing toward the closed valve. The front travels at the speed of sound.
When the front reaches the inlet of the runner, the runner is filled with high pressure stagnant air. At this point, the phenomenon of reverse flow begins. Air begins to flow in the runner, but, instead of flowing toward the valve, it flows from the runner back into the atmosphere (or plenum, if the engine is so equipped). So, another zero thickness front exists, with the air on the inlet end of the runner, flowing back (reverse flow), at zero pressure, into the atmosphere.
When this newly described front reaches the closed valve, the pressure of the air near that valve head acts as you would expect. With the air now flowing away from the closed valve, the pressure drops by that same ρVc amount. When this new front reaches the runner inlet, it should not be surprising that the initial flow conditions reappear.
It is apparent, then, that there exists an optimum number of cycles between valve closure and valve opening. This is when engineers start talking about “third harmonic” tuning and “fourth harmonic” Obviously, we would choose a minimum number of wave traverses. Unfortunately the manifold becomes more difficult to stuff under the hood as we reduce traverses. Jaguar experimented with first harmonic tuning on the dyno and got volumetric efficiency numbers above 100%, but the third harmonic seems to be a good compromise. Of course, that nasty Second Law places some limitations on all of this.
There were equations tossed about at Chrysler, but I have deliberately avoided them here. Well, I'll throw in one: NL = 84000. However, this is only somewhat valid if you're using very “tame” cam timing. The article about “Ramming The Rat” in that highly technical magazine “Hot Rod” (available online) is worth the reading. Yeah, I'm the old guy in the pictures.