This post continues on from an explanation of what room nodes are. We're going to look at them at a slightly higher level.
First off, we have to understand the difference between a room node and a room mode.
A node is a physical point in the room where the resonances at a specific frequency cancel each other out. A mode is the resonance at a given frequency itself. It's a subtle distinction.
In a cuboid (rectangular) room, there are three types of room mode: axial, tangential and oblique.
A simplified way of looking at them is to think of them as the result of waves bouncing off walls in a room: axial bounce off two walls, tangential off four, and oblique off all six. The more walls it bounces off, the less powerful the convergence effect -- but they add up.
The calculation of the frequencies of each is based on the length of the path of the wave. This means that you can work it out via the Euclidean vector product (better known as Pythagoras's Theorem) resulting in Rayleigh's Equation:
Here, L W and H are the length, width, and height of the room respectively. P, Q and R are the harmonic you're trying to calculate. C is the speed of sound (343m/s).
Now that we have this, we can calculate any harmonic of the room modes. As previously mentioned, the more times a frequency converges in different harmonics, the stronger the room node effect is going to be.
So this is a relatively straightforward way to determine the troublesome frequencies in a room. By creating a spreadsheet with every permutation of harmonics, you can determine exactly where to look based purely on the dimensions of the room.