Based on room dimension measurements the modes (or is it nodes?) are at 43Hz, 21Hz, and 70Hz.
My question is what the heck do I do with those numbers? Does it point me to anything specific to address? From what I understand these would be the frequencies that the room hangs on to - so these frequencies should be louder than everything else. Have I got that right? Or is it opposite?
It's both.
A sound wave is an energy exchange between pressure and particle velocity. Where the air particles are at their highest pressure (what you can hear), they're at their lowest velocity. And when they're at their highest velocity (what you can't hear), they're at their lowest pressure.
A room
mode is a frequency where the room is resonant. It happens because the length of the room is a multiple of the wavelength of the frequency.
A
node is a location where pressure peaks of waves overlap, causing an even higher sound pressure (louder). The overlapping waves can be difference pieces of a wave reflecting off of walls. That is why you get nodes at room mode frequencies, because the dimensions of the room, with respect to the speed of sound, cause the sound to reflect back into itself at just the right time.
An anti-node is the same thing, except where pressures cancel out.
You can figure out where a node should be based on the wavelength of a room mode.
Going back to a sound wave being a period exchange between pressure and velocity...
On the surface of a wall, the air particle velocity must be 0. The air can't move into the wall, and it can't move away from it ( or else it leaves a vacuum). So at that location, you have a pressure zone, where the pressure goes up and down but the velocity never changes. (This is why you usually hear a bass boost when you put your ear near a wall or corner.) In a free field the pressure fields move along and don't hang out in a single location like they do at a wall.
If you move away from the wall a distance of 1/4-wavelength, you arrive at the zone of maximum velocity, where sound pressure is at a minimum. The air particles are moving back and forth towards and away from the wall here, but they never develop pressure. You can't hear velocity, only pressure, so at this location the sound drops out. I guess this is what you mean by suck out.
If you move away from the wall 1/2-wavelength, you arrive at the next pressure zone that is always out of phase with the pressure at the wall. This is where the sound will be its loudest.
Now if your room dimensions are such that pressure and velocity zones from sound waves bouncing off of opposite walls line up, you get spots where the sound is very loud and/or spots where the sound is very quiet. These are the nodes and anti-nodes.
The way to solve this is to keep coherent waves of the same frequency from bouncing into each other. This is the reason for building a room with non-parallel walls. It's also why you add diffusers. Diffusers break up the sound waves as they bounce, scattering little pieces of them in all directions.