I think you're phrasing the question wrong.
Your starting statement is what we call "self referential" - if you need a speaker that is "flat and clean from 20 Hz to 20 kHz" then that's what you need.
My answer is that: "it should extend as far as you need it to - whether it needs to extend beyond that, or how far, depends on a lot of different variables".
What you're talking about are more like "generalizations" or "general rules of thumb"...
Like, for example, "if a sub can deliver plenty of output at 10 Hz then it will probably have no problem at 20 Hz"...
And, in this case, that generalization is based on the assumption that a sub will work better "if not pushed too close to its limits".
The catch is that,when it comes to subwoofers, there are simply too many factors involved to allow for useful generalizations...
(And, these days, with things like DSP processing, rules of thumb simply don't always apply.)
There are sealed subs that are rated to 20 Hz but still have useful response down to 10 Hz...
And there are tuned subs that are rated to 20 Hz whose response drops like the proverbial rock below 18 Hz...
But nothing there will tell us whether they will or won't perform equally well at their rated 20 Hz...
And nothing there will tell us which one will sound "musical" and which may sound like "an empty washtub"...
(At worst, if you buy a sub rated to 10 Hz, when all you really need is 20 Hz performance, you're paying for extra performance you may not need.)
And, when discussing full range speakers, there are all sorts of other things that make much more difference than the -3dB points.
For example, a smooth response over the critical midrange region, or minimal ringing and time smearing in the tweeter.
I would also suggest not making too many assumptions when all you have are a few data points.
For example, a typical high-fidelity speaker rated "40 Hz to 17 kHz +/- 3 dB" is probably rolling off to -3 dB at 40 Hz and 17 kHz.
And, since the +/- 3 dB range covers the midrange, it has at least a relatively smooth midrange response.
However, those same specs could apply to a public address speaker, which is -3 dB at 40 Hz, +3 dB at 17 kHz, and +12 dB at 25 kHz.
(But the latter won't be obvious unless you have a few more numbers or, better yet, a graph.)
At any frequency above 10 kHz, the second harmonic is 20 kHz, so harmonic distortion will fall outside the audible range.
(And even IM distortion which falls above 10 kHz may not be especially noticeable.)
However, other types of distortion, like excessive ringing, which is common in tweeters, may be extremely audible.
In the midrange region, where our ears are especially sensitive, most types of distortion tend to be audible.
In the low bass registers it's going to depend heavily on the type of content you're listening to.
For example, if we're talking about the sound of a train wreck, or a Godzilla roar, even high levels of distortion probably won't be a problem.
(Because the sound the special effects guys use for that will probably be mostly jumbled noise and distortion anyway.)
However, with a clean pipe organ bass note, even moderate amounts of certain types of distortion may be audible...
And, with a clean low note coming from a synthesizer, that will be even more true...
And any study on the subject would have to use enough different samples to cover all of those possibilities...
No, and that's not the point.
And that brings up a good, but seldom-discussed question - How far beyond the expected program bandwidth must a speaker's response extend? If we use the conventional program bandwidth of 20-20kHz. then an extra octave on each end would be 10-40kHz. response from the loudspeaker. This seems excessively demanding. But if we limit the speaker's requirements to only a half an octave beyond the program, we get 15-30kHz. Still difficult, but not impossible.
However, the VAST majority of speakers can't meet the half octave surplus either. In fact most speakers have -3dB responses of closer to 40-15kHz. Even with a "subwoofer," the -3dB only goes down to about 30. Equalization can compensate to some extent, provided that the speakers' power handling is adequate, but at the expense of excessive distortion. Some argue that distortion at the frequency extremes is not audible, but I've not seen any studies confirming that (not to say it isn't so - just that I don't know if it's proven).
So to repeat the question - how far should a speaker's response extend beyond the anticipated music bandwidth in order to both avoid excessive distortion and to cleanly reproduce all program frequencies?
KeithL ?
Boomzilla