Acoustics and Low Frequency Damping pt. 5

Now we move on to 3-dimensions and see how to further increase the effectiveness of our bass trapping. Remember, pressure-zone-absorbers (like TubeTraps) work best in – you guessed it – pressure zones. Read on to understand the method by which YOU can control the decay times of the resonant frequencies in your room. From the AES paper titled as above, by ASC Owner & President, Art Noxon, comes another excerpt from this enlightening piece. Enjoy!

View the entire paper.

Three Dimensional Modes

The three dimensional model of Pressure Zone Trapping also has a primitive cell, (1,1,1). It has eight corners, each containing a quarter wavelength pressure zone. If all eight zones were placed together a complete sphere would be formed.

Harmonics of the fundamental are built in terms of complete cells. The (1,1,2) will be one cell high, one cell wide, and two cells deep. It will have 8 x 2 or 16 pressure zones. The (1,1,3) mode is one by one by three cells in configuration and has 8 x 3 or 24 pressure zones.

The (2,2,2) mode is accordingly two by two by two cells for a total of eight and 8 x 8 or 64 pressure zones. The total number of pressure zones for any (L,M,N) mode is 8(LMN). They momentarily hold all the energy of the resonant field two times per cycle for any standing wave mode in a three dimensional field.

The basic Pressure Zone Trapping formula still applies. The more complicated term for frequency, well known and dependent on three terms, can be substituted. The value for absorption coefficient remains the fraction of energy absorbed per absorption event. It is the fraction of trapped zones times the efficiency term.

The formal RT60 equation can be simplified if the absorption coefficient is less than 1/5 by approximation. The complete RT60 equation is written by substituting terms for frequency and fraction of energy. This formal equation can be simplified if the absorption coefficient (F) is less than 1/5 in the log term.

The RT60 equation can be further developed. The room volume (Vr) term is introduced which converts the three mode numbers into wave numbers.

Wave Number Space

Wave number space is a three dimensional coordinate system with A, B, and C axes. Each point (P) in this space defines a resonant mode for the room. This is not a continuous field space. It is more like a crystal; discrete points set apart at specific distances.

The mode point is at the tip of the resultant vector (D) whose magnitude is the sum of the squares of the components. It is also at the far corner of a rectangle whose volume (V) is known by the products of its components.

The frequency and RT60 formulas can be rewritten in terms of this wave number space geometry.

This listening room already has a decay time. Frequently improvement in the decay rate is desired. The minimum upgrade is to trap one zone for each 500 cubic feet of room volume. The resulting RT60 is a simple expression but is only valid for an absolutely rigid room whose only absorption is due to the trapped zones.

Example:

Consider a room 18 by 24 by 8 feet high. We can look at mode (2,2,1). The wave numbers (1/9, 1/12, 1/8) are easily calculated along with the volume and diagonal wave number in space. The decay time for that mode is 0.3 sec. This assumes one 100% efficient absorption device per 500 cubic feet of room volume.

These are the straightforward calculations used to “dial in” your room sound and create smooth, musical bass so you can hear your speakers and recordings as they were intended. No partial derivatives or triple integrals, just your rooms dimensions and some basic arithmetic. You can do it!

Now, what if the absorption device is not 100% efficient at a given frequency? And what is the Q (quality factor) you should be aiming for?