Rick,
You are absolutely correct! I left the word out -
accurately - IOW; it is impossible to reproduce 20 Hz accurately in a room that does not have ONE dimension of at LEAST about 38 feet.
Sorry about that folks! and Thank you Rick for pointing this out.
To put it simply;
It is important to understand something about Critical Distance, Bass trapping, and the pressure zone of the room.
Side note:
Far too many people build look-alikes or copies. These usually have a diamond shape copied from Peter D'Antonio's RFZ designs, others copy different pieces of other designs that they like alot. A few get lucky, most do not. What is usually missing is the 'understanding' of what any particular design parameter does to the whole. Because a studio is not a collection of rooms, treatment, and equipment; it is a system. This system must function as a whole to work properly. But I digress.
Critical distance is defined as the distance that sound ceases to fall off at -6 dB per doubling of distance from the source. The source sound goes constant volume at it Dc (Critical Distance) - and the volume is the same everywhere in the room. This translates to 'MUD'.
It is extremely difficult to treat and/or trap sound that is in the pressure zone. Producing sound waves that exceed the dimensions of a critical listening room will only tend to mud things up. That is why I set the optimal dimensions for a 20 Hz room at about 38 feet. The full length of a 20 Hz sound wave is 56' - 4". Divide that by two and you get a half-wave. This is the lowest mode. A quarter-wave would fall into the constant volume of the pressure zone, IF YOU ARE IN A CONCRETE ENCLOSURE.
So, I take 20 Hz and multiply by the reciprocal of (SQRT)2 and get 14.1 Hz - The half-wave length of this is 39' - 10". That's where I get the 38 Feet. - It ensures a smooth transition from 20 Hz to the pressure zone and allows an easy roll-off on the sub.
Smooth response in the LF range from 20 Hz to 250 Hz detemines the quality of the room. This is the very reason why so many of the old control rooms sound very good. They are huge and the dimensions support a dense low frequency modal distribution.
So, if you can't get the size/volume then you have to be very careful about what to expect from frequencies below this dimensional threshold. (LOL - sounds like star trek) By dimensional, I mean Room Dimensions / room boundaries.
Another way to look at the pressure zone and the effects of critical distance is similar to what is experienced with Speaker-Boundary-Interference-Response and simillarly Listener-Boundary-Interference-Response. - Imagine yourself inside a perfectly polished mirror box with 6 sides.. floors, ceiling, and all the walls are mirrors. There you are standing or siting in you 'mix position'. Look around (if the walls are perfectly parallel) you will see 6 more of YOU. Now, put your speakers in their place.. HOLY COW! look at all those speakers now! So, in addition to your speakers, there are 12 more of them PLUS their multiple reflectons that go on forever into the distance!
Next imagine playing all of those speakers at the same time. You actually really DO this in an untreated room. THAT's what you're hearing!
Here's a thought for you; What if your walls, ceiling and floor are not exactly parallel, you could (theoretically) reduce the mirage images down to once on each surface, but I am not a fan of that approach as there are far too many variables and as humans, we don't like to sit with our head clamped in a vice. We like to move around.
Sorry, I get carried away on things..
So a pressure zone experience will be like bringing the mirror back in after the room is treated.. only for those lower frequencies. ok? That's where the mud comes from. I hope that you get the picture that I'm trying to paint. I don't want to put up crazy formulas that most people won't get. We designers often put up lots of the formulas to impress other designers. - Reminds me of a saying that I heard in Nashville - "if you can't dazzel them with brilliance - baffle them with bullshit!" I'm not gonna do that. ok?
More to come...
Cheers,
John