Reading: Speaker and Room - 2

The room acoustics wiki page defines things pretty clear. There are four regions regarding the room. The first region is the frequencies below the lowest resonance frequency of the room. The second one starts from the first resonance frequency to the Schroeder frequency. Next one is a transition region and extend about two octives beyond. Lastly, it is the ray-like region.

Schroeder frequency is the critical point between ray-like behavior and room mode behavior. There's a empirical formula to derive the frequency using room volume and the RT60, the time took the signal to decay to a non-audible level, which can be measured using REW, a free software. And these two articles, Part I and Part II, give some recommendation upon using sub-woofer considering the facts about Schroeder frequency and the human capability to localize a sound source. In short, he suggest to use a 80Hz cross-over with equalization. He also pointed out that the amplitude of a room mode across the whole room will vary a lot, thus the EQ will only works at a particular listening position, or a sweet region at best.

Under the lowest mode, the room only experiences static pressure, which means open baffle speaker at this operating range will produce nothing you can hear, cause the two opposite phase waves totally cancelled in the room. We either choose a wall mount speaker to leave the backward wave outside the room or use a closed cabinet to keep the backward wave inside another small box. The latter explains why most sub-woofer are close cabinet design just in case you have a very small room.

From the first resonance frequency to the Schroeder frequency is the mode dominant operating band. Bass trap and room treatment are some tools we can use to tame the crazy null and peaks in this range. I tend to believe a normal living room with all the things you like within will decrease the quality factor of the resonance modes and leads to dull peaks and nulls. A slow variation in the frequency response may be cured by equalization but a small room with a lot of sharp peaks and dulls cannot be cured using EQ. They are so dense in spectrum thus the 1/3 octive EQ cannot catch it. Some room treatment or bass trap is must.

For the last region, the acoustic radiation pattern of the speaker matters and we will try to tame all reflections, but special effort should be put on those reside within 2ms of the direct sound,which will make the image fuzzy. Broadband absorbing panel , carpet and wall decorations will help in this region.

At last, comb filter. It is the inference from a point source in front of a flat wall. The reflected wave will constructively or destructively interfere with the original wave and result in dense peaks and nulls around low frequencies. On cure is to use a diffusive front wall (in listener's point of view). Another is a dipole speaker with optimal listening position, where your distance to the back wall is the same as the speaker to the front wall. I learned this again from Linkwitz Labs Q31. The last resort is to put the speaker right against the wall. This may introduce some unwanted room mode but some speaker really shines at this position, like Big is Better.

Regarding RT60, this article from RealTraps has a few insightful notes. The key point is that audio engineering process the sound with RT60 of the listening room in mind. For a home theater with 5.1 or 7.1 surround system, a short RT60, around 200ms~300ms is appropriate since the "echos" will comes from the satellite speakers but not the room. For most stereo music, 500ms is a good number.

Let me turn back to my one wavelength criteria. I tried to argue that when the wavelength is considerable to the room size, the far field analysis gives us little information and the coupled speaker/room combination must be considered. I feel the criteria is not that appropriate since it is enforce to have a valid large spherical Hankel function approximation but not to deal with room mode. The Schroeder frequency is the better indicator. After reading the two articles regarding Schroeder frequency, I believe that stereo sub-woofer is the way to go but the placement must be corrected. They should be placed to deliver the flattest bass response and the direct path length difference between the sub-woofer and the mid-range to the listener can be corrected by digital delay. I feel this is still a must since it will effect the time step response a lot. I want a fast bass but not listening to a bass single tone that builds up energy in the room. In such an approach, stereo sub-woofer with digital delay should keep the image good beyond 80Hz (I don't know where this number comes from) and also have a smooth bass below Schroeder frequency due to the placement.