
To find the frequency that lies halfway between two other frequencies, multiply one times the other and take the square root: Below are the mode frequencies for the test room, along with the center frequencies we tested. Modes not identified as Tangential (Tan) or Oblique (Obl) are Axial. Due to physical space constraints we were unable to place balloons at every nonmodal 1/4 wavelength distance from the rear wall. So we picked those few frequencies (highlighted in bold below) that had the greatest distance to neighboring frequencies to minimize the chance of exciting an adjacent mode.
Room Modes calculated by: www.mcsquared.com/modecalc.htm 
WELCOME Welcome to the RealTraps Quarter Wavelength Party. Your hosts are me, Ethan Winer, my fabulous RealTraps partner, Doug Ferrara, and our most excellent friend Chuck Scott who's handling the video cam. We have balloons, sine waves and standing waves, and lots of other cool stuff on hand. We're here in the control room of Doug's home studio, and for this presentation Doug has removed all of his furniture and acoustic treatment  even the carpet. This will reveal the room's characteristics as much as possible for the experiment that follows. The main purpose of this demonstration is to show why broadband absorption is the best way to treat low frequency problems in small listening rooms. The conventional wisdom is to determine the room modes based on the room's dimensions, then design custom bass trapping to target those specific frequencies. Top There are two problems with this approach: Even if you consider only the first five axial modes for each dimension, that still requires building bass traps for fifteen different frequencies! Just as important, all rooms exhibit peaks and nulls at all frequencies, not just those that correspond to the room dimensions. The notion that standing waves exist at all frequencies has been the subject of heated debate in the online acoustics forums and newsgroups. Many people wrongly believe that peaks and nulls occur only at frequencies whose wavelengths can exactly fit within the various room dimensions. For example, if a room is ten feet deep, then that dimension will allow standing waves only at 56.6 Hz and its multiples, like 113 Hz and so forth. But that's simply not the case, as the following experiment will prove. In truth, acoustic boundary interference causes nulls at approximately 1/4 wavelength away from many of the room's surfaces. Especially near the back of the room, it is easy to locate a null one quarter wavelength away from the wall at any frequency. Top These days many people mix in very small rooms, which means they're always near to one or more walls, not to mention the floor and probably the ceiling too. When choosing acoustic treatment to flatten the room's low frequency response, it's significant that peaks and deep nulls exist at all frequencies near the room boundaries. The basic mechanism works like this: When a sound wave reaches a rigid surface, it is reflected back toward the source. At a point one quarter wavelength from the wall, regardless of frequency, the total round trip is one half wavelength. Which is the same as 180 degrees out of phase. In order to create a null of any magnitude, the opposing signals must be very similar in level  that is, equal but opposite. And for this to happen the surface must be reflective at the frequency of interest. Top Let me make one other point before beginning the demonstration: Some people question the use of sine waves for audio testing, claiming it doesn't represent real music. But sine waves are in fact very similar to real bass instruments. When an electric bass sustains a long note in a slow ballad, the primary components are the fundamental sine wave and the second harmonic sine wave. So it's not a big leap to use sine waves, whose frequency and amplitude can be better controlled to allow accurate and repeatable measurement. As you can see, we've set up some balloons near the rear wall. This room is exactly 16 feet 3 inches long, by 9 feet 91/2 inches wide, and 7 feet 8 inches tall for most of the length. We calculated all of the axial, tangential, and oblique modes up to 300 Hz, and then selected frequencies that do not correspond to any of them. By carefully selecting frequencies that fall exactly between mode frequencies, we can establish that standing waves and their associated peaks and nulls exist at nonmodal frequencies. Top These balloons identify the nulls related to 1/4 wavelength from the rear wall. Another balloon near the mix position shows that nonmodal nulls are damaging there too. We put the balloons here earlier to save time now. One by one Doug will play a frequency, and I'll move the microphone into the null. The mike goes to this laptop computer, so you can see the nulls. [demonstration portion] Finally, I'd like to thank Wes Lachot for documenting the issue of 1/4 wavelength cancellations so well in his article in TapeOp magazine. Wes couldn't be here tonight in person, but he's definitely here in spirit. I also want to thank Doug, and Chuck Scott. Top [end of video] Now that we've proven nulls can exist at any frequency in any room at a predictable distance from the boundaries, two other points should be made. First, besides having nulls at one quarter wavelength away from the wall, there are other nulls at other multiples. For example, there will also be a null at three quarters wavelength, and at one and one quarter wavelength. For example, the 121.7 Hz null at the mix position in this video is 3/4 wavelength from the rear wall. There are also peaks at one half wavelength away, one wavelength away, and so forth. Second, it's important to explain why the location of each null is so localized. This is because all small rooms have dozens of reflections that interact and disrupt the critical balance needed to create a null. As was explained in the video, the wavefronts must be opposite and very nearly equal to create a severe null. These nulls are related not only to the distance from the rear wall, but also from the other walls, the floor, and the ceiling. So in order to create a deep null a precise balance is needed, and that balance is easily disrupted by the many other reflections bouncing around the room. However, the main point to be made is that the basic principle of acoustic boundary interference is indeed valid. Thanks very much for watching! Top 
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