The Science of Subwoofing Page 4

The limits for Doppler distortion were also investigated by Fielder and Benjamin. To refresh your memory, Doppler distortion is frequency modulation of the higher frequencies by the lower frequencies being reproduced by a single driver; something like tape flutter except that here the music or cone excursion provides a constantly varying modulating signal. The bottom line is that, for practical cone excursions, and with the bandwidth limited to 12.5Hz to 100Hz, the FM distortion due to the Doppler effect appears to be far below the threshold of audibility. Thus the harmonic distortion guidelines stated above appear to be the really important distortion criteria for accurate subwoofer performance.

Various combinations of 12, 15, 18, and 24" woofers were tested by Fielder and Benjamin, and none were found to satisfy their distortion criteria at 20Hz and 92dB SPL, 50Hz and 108dB SPL, and 100Hz and 101dB SPL. Several of the subwoofers tested used multiple drivers in an attempt to improve power handling and linearity at low frequencies, but unfortunately the drivers were so nonlinear to begin with that even this attempt failed to meet their criteria. The authors sadly report that it is evidently believed in the loudspeaker industry that woofer distortion is not particularly important; as a result, there are very few drivers built that possess adequate linearity. All of this bodes ill for our chances of finding the ideal subwoofer from a commercial vendor.

Low-Frequency Performance of Small Rooms
All rooms exhibit a set of natural resonance frequencies which are related to the dimensions of the room. The room will respond strongly to those sounds having frequencies close to these natural frequencies. Once they are excited, the result is a set of standing waves, each wave having its own spatial pattern of nodes and antinodes. These standing waves form the room's reverberant field, which is part of the soundfield received at the listening seat. So, unless you're listening in an anechoic chamber, which by definition only contributes direct sound, every room invariably superimposes its own characteristics on any sound source present. Room modes are classified as either normal, axial, or oblique—depending on which room boundaries they graze.

It is possible to estimate the number of normal modes in a given room for a particular frequency band.$s2 The number of normal modes is linearly proportional to the volume of the room, but increases as the square of the frequency. At higher frequencies, an enormous number of standing waves is generated. These overlap, blend together, and thus smooth out the room response. At the lower frequencies, the only way to generate a large number of modes is by increasing the volume of the room. In a concert hall there are thousands of modes below 100Hz, whereas in a small room there's a paucity of bass modes. For example, in a rectangular room 10x15x20', the natural frequencies below 100Hz are as follows: 27.5, 36.6, 45.9, 55.0, 61.5, 66.0, 71.5, 73.2, 77.5, 78.5, 82.5, 86.0, 90.2, 91.5, 95.5, and 99.0Hz. The net result for this modal sparseness in a typical listening room will be uneven, and hence colored, bass reproduction.

I've painted a pretty bleak picture for the possibility of accurate bass reproduction in small rooms, and the temptation would be to throw in the towel and accept the natural order of things. This would be a mistake. There's an old saying among chess players that you can't win by resigning. No matter how bleak the prospects are, there's usually one final trap or long-shot resource to try out. In our case, there are, in fact, a number of worthwhile resources available. First, if you have the choice, avoid a symmetrical room; eg, a cube. The response of the room becomes less uniform as its symmetry is increased. Next, it pays to experiment with damping materials and subwoofer placement in the room. If there's a particularly nasty room mode you'd very much like to minimize, try placing the subwoofer in a pressure node or minimum for that mode. In this location, the problem mode will only be weakly excited by the subwoofer. Of course, this presumes that you have the freedom to move the subwoofer about.

There is, however, one location you must avoid at all costs, unless you're more concerned with efficiency than accuracy. Each of the individual standing waves in a room can only be fully excited by a sound source located in a pressure antinode or maximum for that wave. And it so happens that in a rectangular room, the pressure amplitudes of all standing waves are maximized in the corners of the room. A subwoofer in the corner will be able to strongly excite every possible room mode. This blows away the myth that subwoofer placement is not critical and that it may be safely tucked away out of sight in a corner. I realize that the lows are not directional, so that it would be possible to get away with a corner placement without horribly screwing up the soundstage. But what a price to pay! I suspect that this myth was hatched long ago by a manufacturer anxious to soften spousal resistance to the presence of a rather large and conspicuous box in the living room.

The final resource is the use of absorbing materials or wave traps to dampen the amplitude of room modes. Generally speaking, an absorbing surface is most effective in damping a normal mode if it is located in a region of pressure maxima. Because all normal modes have pressure maxima at the corners, absorbing material placed near the corners of a room is twice as effective on the average as alternate placements.

There is another practical problem affecting the accuracy of bass reproduction in small rooms: boundary effects. A small room is much easier to overload with acoustic energy than a large room. This means that structural rattles, buzzes, and wall resonances would be more prominent in a small room. Again, much of the sonic signature of wall resonances can be controlled by lining walls with absorbing material. I have used foam and 1"-thick fiberglass panels (they're cheap) to control room modes and wall resonances. The difference this treatment has made in my room is simply astounding. Without it, the upper bass is highly colored—no matter how accurate the sound source. If your lifestyle allows it, do your ears a favor and go for it.

The Art of Matchmaking: System Integration
It has been some 250 years since Jonathan Swift's Captain Gulliver tangled with the inhabitants of the land of Lilliput. In the interim, it appears to me that a significant number of Lilliputians have succeeded in infiltrating the British Isles. How else am I to account for the uniquely British craze for miniature loudspeakers? The BBC, rumored to be a Lilliputian stronghold, started it all when they licensed commercial production of the LS3/5A minimonitor. The ProAc Tablette followed shortly thereafter, and managed to infect the minds of audiophiliacs on this side of the Atlantic.

The situation has progressed to the point where recently the Acoustic Energy AE1 minimonitor, with a truly Lilliputian 4" woofer, made Stereophile's list of recommended components. A 4" woofer? Give me a break! How can anyone mistake a midrange driver for a woofer? Is it even fair to advertise these wooferless designs as loudspeakers? Well, maybe. Having by now punched a fair number of readers' buttons, I have to confess that I'm actually sympathetic to the Lilliputian Legacy: smaller can be more nimble and cunning.



Footnote 2: See "The Acoustics of Small Rooms," The New Audio Cyclopedia, Howard W. Sams & Co., pp.43 through 53.
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