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.

Reading: Speaker and Room

I am thinking about to DIY my audio system and digging into the speaker design as the first step. I am intrigued by open baffle design cause people said it gives a very airy and open sound. Linkwitz Lab has a very detailed analysis and discussion about dipole speaker and open baffle is one of many implementations.

He designed the speaker with equalization in mind thus he operate the speaker BELOW the first resonance frequency. This is a very different approach. I heard people around different discussion boards saying that larger baffle gives a deeper bass. It suggests they are operating ABOVE the first resonance frequency.

Once you operate above the first resonance, the oscillation in the frequency response comes naturally. As the length equals to a half wavelength, the waves from the front and back add up. When the length equals a full wavelength, the waves cancel. This issue is not that severe using a real driver comparing to the piston model analyzed since the speaker cone gives an asymmetrical response in front and in the back. The bracket and the magnet of the speaker also reduces the airflow on the back size, although the bracket and the cone may generate another resonance and a notch filer is required.

For my understanding in antenna, the distance from the observer to the source has to satisfy two conditions for the far field approximation to be valid. First, 2D^2/lambda, where D is the largest dimension of the radiating source and lambda is the operating wavelength. Second, they have to be at least one wavelength apart. Assuming the speakers are 2.4m apart, as suggested in the room acoustics section on Linkwitz lab, and a triangle listening position, the one wavelength criteria is about 140Hz. I believe the acoustic property is dominated by room mode and near field property of the speakers below this frequency. It leads to the conclusion that a sub-woofer should be used with a 140Hz crossover frequency. Please bear in mind that I am assuming a pretty small room and a pretty close listening position. Once you move to a large room, not only the room mode frequency decreases but also the far field is still valid. Things are back to acoustic pattern again.

Art Ludwig's website gives excellent discussion about room mode based on his own image theory code. Mr. Ludwig and Mr. Riley are on the two ends of a spectrum regarding listening room. Mr. Ludwig has a nearly empty listening room with a lot of treatment while Mr. Riley uses a normal living room. The analysis performed by Mr. Ludwig shows that a "bad room" is not much worse than a "good room" but both of them are far from an optimal flat response. I didn't find the suggesting regarding this fact. On the other hand, Mr. Riley believes that human brain can process a "uniformly" excited room with normal furniture and decoration inside. Since I don't have a room dedicated for listening, I can only believe what Mr. Riley said and will choose to use stereo sub-woofers along the two side walls at a distance to the listening position the same as from the main speaker to the listening spot. This placement is learned from the Pluto+ sub-woofer. The position is chosen to lower the excitation of the room mode (instead of placed at the corner of the room to excite the mode to the most level) and keep everything symmetrical. Symmetry is a beauty and it even works for near field. I would love to keep it whenever I can.

I take the advice from Mr. Riley and try to keep the main speakers at least 1m away from ANY wall. I will also keep the room as comfortable as I like.