Slat-type Helmholtz absorbers are very easy to design. The formula for calculating the absorber's resonant frequency is:
f = 2160 * sqrt ( r / (( d * D ) + ( r + w )))
Where:
f = resonant frequency of the absorber in Hertz (Hz)
d = effective depth of slot in inches (1.2 x the actual thickness of the slat)
D = airspace depth (depth of box behind the slots) in inches
You can use a spread sheet such as Microsoft Excel to model various dimensions and tunings for slat-type Helmholtz absorbers. This can be very useful as you can easily see how changing any dimension changes the tuning of the absorber.
The formula for determining the fundamental frequency of a standing wave for a particular room dimension is:
Where:
fo = Fundamental frequency of the standing wave
V = Velocity of sound (1130 feet per second)
d = Room dimension being considered in feet (length, width, or height)
Other standing waves occur at harmonics of the fundamental frequency - that is 2, 3, and 4 times the fundamental. Thus a room with an 8 foot ceiling has standing waves forming at 70 Hz (the fundamental frequency or first harmonic), 140 Hz (the second harmonic), 210 Hz (the third harmonic) and 280 Hz (the fourth harmonic).
As mentioned earlier, rooms with smaller dimensions often have standing waves or resonance build ups that are very noticeable causing coloration at around 200 Hz or so.
For example, building a box with an airspace depth of 4 inches using wood slats 1/2 inch thick and 2-1/2 wide results in a box tuning of about 240 Hz. In practice it is not usually necessary to be extremely exact with the tuning frequency. Being in the ballpark will often work very well. In fact many slat-type bass traps are designed with slots of varying widths (perhaps plus or minus 1/16 to 1/8 inch of the design center frequency) to cover a wider band of frequencies. Also loosely lining the inside of the box with materials such as fiberglass widens the bandwidth (lowers the Q) of the absorber. Building and mounting multiple units perhaps with slight variations in tuning can also improve the control of coloration. Mounting multiple units throughout a room improves absorption effectiveness and promotes diffusion of higher frequencies.
A more complete explanation of the principles of acoustics mentioned here can be found in Jeff Cooper's book entitled Building A Recording Studio. It is a fairly basic and easy to understand book on acoustics, and it is also very practical and very useful for someone interested in building a small recording studio.