My take subwoofer speed;
Somewhat like porn, except in this case ... you know it when you hear it
Terms like "speed", "tight", "taught" "quickness", or more maybe appropriately "well defined, well delineated, transparent or high resolution bass".... etc, enthusiasts, savvy or otherwise will continue to use the terms.
The time domain.
It's a function of several elements. But as mentioned, it's the time domain that's key to the subjective appeal of subwoofer speed. It's a well executed and capable sub design that's matched ideally in time/signal alignment with the octaves above. As Bill stated, material like a bass guitar has complex variety of harmonics, ... all of which must be aligned in time for an accurate portrayal of the instrument.
A kick drum, a rock kick drum heavily EQ'd may have a spectrally diverse set of components. Typically boom, smack, click .. is often what engineers may use when discussing it. Anyway, artificial or not, it's ideal if it's all aligned upon the wave-launch into the room. If the time alignment is off, the subjective component lost is speed, definition, spectral delineation.
On the room side, there's a host of acoustic distortions .. that can easily corrupt the signal that was so well aligned aligned a short time ago. SBIR or any destructive acoustic influence can easily null an important spectral component of the kick drum/bass guitar,..so care must be taken. Also, a room's decay characteristics are of paramount importance in subjective appeal for speed, definition and tightness. Unfortunately, decay characteristics for the bottom octaves are contraindicated for the midband and upper freqs (but there's steps that mitigate this issue).
Finally, the system's capability comes into play. Velocity has been mentioned, as has ringing. Maintaining adequate system headroom with multiple drivers, so that each driver moves slower (yes slower
) for a given freq/given level .... thus lowering potential non-linearity and the artifacts contained therein.