It must be said that cabin gain should not be confused with a single resonance of any environment. In any environment a resonance occures though, but is not the entire idea behind cabin gain. Within an enclosed area, even your subwoofer box, resonances do occur, that not even the golden rule can control. It is based on the build up of pressure from sound waves at specific frequencies correlating with specific distances, much like the common known transmission line tuning idea, which that is even more complex than a resonance and should not be considered a tuning at all. Nor should an enclosure with reflection paths. I.e. your vehicle. As we know, each frequency has its own length of propagation. For this, the full wave propagation is frequency dependant. This is why different volumes of compression has different excited frequencies (modes), such as your vehicle. So, at these distances, once met with the full wave propagated frequency, a mode occurs. The actual cabin gain in a vehicle is due to an acoustically small compression in relation to low frequency response. Because frequencies below 150Hz, known as Bass frequencies, are much longer in wavelength than any dimension of your vehicle. So, because the wavelength is longer, it is cut into pieces when propagated to full distance of the wavelength. This seperation causes the frequency of interest to travel the same path of propagation more than once. Since timing and reflection losses come into play based on distance traveled, these wavelengths add to the output of the original propagated path of sound from the frequency mode, and creates the gain of that frequency at specific points in the environment. Until the point where the frequency drops output tp -60d+, it adds to the original response gain. It is at these full wavelength distances that this occurs, and within half the distance, as well as a quarter of the distance. It is because of this acoustically small environment that we consider quarterwave theory more of an interest. Because we are able to fit quarter waves into a vehicle in most cases.
Though there are no general rules for calculating cabin gain, the reflection losses, as well as dampening that occurs during this propagated signal, can be figured for using very complex algorithms related to decibel pressure and intensity. For this, cabin gain can be figured for every frequency in the spectrum, as long as we know the distances each frequency travels, the time it takes to travel that distance, the losses involved, the position of the point of reference and point of listener, and the point of -60dB referenced at a specific location, we can figure for what each frequency does when it causes gain from reflection. And because different propagation paths exists, mainly omnidirectional, which creates a near virtual infinite propagation path, seperated by direct propagation, and three other main propagation techniques, we can calculate the gain of every frequency at every point in the vehicle.
This allows us to then fully gain a more accurate idea of sound intensity based on an entire response at each position. That is the basics of cabin gain and what it does for us. Now, explaining each part of it is a different story. If anything is off, such as dampening factors of specific materials, then the response gain becomes less accurate.
Here is the kicker that helps us in car audio.....because it is based on compression and expansion, we can reach a point where cabin gain is less important. An example would be utilizing 12 12s in a crx for example. With a proper enclosure and compression ratio between the enclosure and cabin volume, cabin gain becomes great at all frequencies in the passband, and acts much like being inside a box, where two great things happen...1. Phase issues are reduced majorly, and 2. Response smoothness increases majorly. This is why doing this is not considered great designing in my eyes, because anyone with basic carpentry and electrical skills can obtain this. Its when the ratio of enclosure to cabin is not equal to balanced compression where the design can become cabin dependant, and relying on gain is essential. Those are my basic thoughts on it all.....so far.
