The Science of Subwoofing

There was a time, as recently as 40 years ago, when frequencies below 100Hz were considered extreme lows, and reproduction below 50Hz was about as common as the unicorn. From our present technological perch, it's too easy to smirk condescendingly at such primitive conditions. But just so you're able to sympathize with the plight of these disadvantaged audiophiles, I should tell you that there were two perfectly good reasons for this parlous state of affairs. First of all, program material at that time was devoid of deep bass; not because it was removed during disc mastering but simply because there wasn't any to begin with. The professional tape recorders of the day featured a frequency response of 50–15kHz, ±2dB—just about on a par with the frequency performance capability of a cheap 1988 cassette tape deck.

And then there were the phono front ends and the loudspeakers of the day. Unsophisticated cartridges and a generally highish cartridge/arm resonance frequency made transduction of the lowest octaves almost impossible. How well do you imagine LF groove modulations can be tracked when the arm/cartridge resonance lies at 30Hz? Loudspeaker bass alignments tended toward high Qs, emulating one-note "boom box" response in the naive belief that quantity was ultimately superior to quality. This was a time when the bass-reflex design was routinely abused, so much so that the name became synonymous with loose and overly resonant bass response. Against this backdrop, limited-frequency program material was really a blessing in disguise.

Ironically, as both home and professional equipment improved, program material failed to keep parity. Oh, I can think of several exceptions, but on the whole records continued to be mastered with very little in the way of deep bass; this time primarily because of commercial considerations. Sure, there's very little musical information in the deep bass, but I believe that, combined the LP's problem with cutting large vertical groove excursions, the prospect of being able to cram more music per side entrenched the practice of mastering with bass summing and rolloff. And because the average home system was still deep-bass deficient, only the audiophiles complained.

The advent of the compact disc has changed all that. The audiophile, after finally purchasing a CD player, quickly realizes just how inadequate his mini-monitors or postage-stamp ESLs really are in handling the potential bass extension and power of this new medium. But being wiser than the average consumer, and thereby realizing that man does not live by bass alone, he's not as likely to alter the status quo of his speakers. The average consumer, however, is much more likely to be fazed by the fact that his bookshelf speakers are not "digital ready." And either the paranoia of "missing something," or the desire to capture the full fidelity of those infamous Telarc cannon shots, a Boeing 747 taking off in his living room, or some such similar sonic spectacular, finally drives him to consider a subwoofer. As we shall see, these are precisely all of the wrong reasons to purchase a subwoofer.

Bass Terminology
So that we all speak the same language, allow me to take a brief detour to examine the objective and subjective terms used to describe the bass octaves. I define deep bass as the range from 20 to 60Hz. In terms of acoustic instruments, only the pipe organ, the bass tuba, and the double bass have any dominant spectral energy in this range. But this range is also very important for the proper tonal balance, or body, of the cello and piano.

The octave from 60 to 120Hz I take to constitute the midbass. Again, the double bass, cello, and piano figure prominently in this range. Add to this list the bass drum, synthesizers, and bass guitar.

Finally, the range from 120 to 240Hz defines the upper bass. This territory represents the heart of orchestral bass, not only because of obvious bass contributions from drums, strings, and piano, but also some of the woodwinds and brass. An excess of energy in this range may be described as thick, mellow, or heavy-bodied sound, while a deficiency of energy in this range lends a thin or lean character to the sound, as it also does in the midbass region. A fat midbass may be best described as tubby, boomy, or as possessing a grunting quality. Because of the ear's rapidly diminishing sensitivity in the deep bass, and the fact that physical sensation begins to play a part in perception, the deep bass is sometimes referred to as belly lows. But even more important than flat frequency response down here is the criterion of dynamic range.

"Punch" or "slam" describe the dynamic performance of a speaker in the mid- and deep bass when it is able to faithfully execute a bass transient. Inherent to such performance is the woofer's excursion capability or its ability to move the requisite volume of air. When a speaker is unable to meet the brutal excursion demands imposed on it in the LF domain—excursion is quadrupled for each halving of the frequency—the result is usually not only a wimpy or polite bass quality but also gross distortion on heavy peaks. As the woofer's suspension is driven into a nonlinear region of operation, a lot of harmonic distortion is generated. The most prominent distortion product is generally the second harmonic, an octave higher, and at sufficiently large cone excursions the woofer's acoustic output may actually be dominated by the second harmonic. This situation is referred to as bass "doubling."

This leads me to the areas of finesse in bass response, areas often overlooked in favor of frequency response and bass power considerations. I'm talking about bass speed, tightness, pitch definition, and resolution of bass detail. These attributes may be more appealing to the music lover who is certainly not immune to the emotional impact of bass power and thunder, but who nonetheless craves a commensurate dose of bass subtlety and delicacy. Most of these things have to do with the absence of low-Q resonances in the bass response of the speaker. These resonances may be generated by the woofer, the box cavity, or by flexure of the cabinet panels. The end result is a muddying effect whereby detail and pitch definition are obscured. The point is that these resonances stay around long after the trailing edge or decay portion of the input signal has ceased, ringing while new transients are being presented to the speaker. In essence, these resonances fill in the silent gap between adjoining transients with sonic garbage. It is this garbage or mud that masks bass detail and detracts from the purity of pitch definition.

Interestingly enough, as Floyd Toole has pointed out, some low-Q colorations may contribute no more than a 0.5dB bump to the frequency response and yet be quite audible. This means that it would be difficult to objectively discern the presence of such resonances from merely examining a speaker's frequency response. What would be much more useful would be a three-dimensional plot of amplitude as a function of frequency and time. These are the type of measurements pioneered by the late Dick Heyser. Such data would indeed show up resonances as ripples in the amplitude response as a function of time. However, even at this level of sophistication we would still be unable to resolve the subjective significance of the various resonances (there will always be some) without comparative listening tests. So our ears and brains must be the final arbiters. Contrary to Consumers Union's claims, speakers that appear to measure alike in the frequency domain may differ significantly in sound quality—even at drive levels that produce negligible distortion products.