Does that mean that it performs at it's best at anything between that or is one of those a sweet spot.
All depends on the listener's personal preference. Typically, manufacturer's will recommended boxes on the smaller side (higher Qtc) because it gives a nice bump in the output in the upper bass/lower midbass region, which is what gives subs a "tight" or "punchy" sound. Plus, that hump in output works out nice for the rap/r&b crowd, which are the main purchasers of subs.
Can the t/s perameters shed any light?
Exactly //content.invisioncic.com/y282845/emoticons/smile.gif.1ebc41e1811405b213edfc4622c41e27.gif That's typically how proper box sizes are determined.
Yes, each box size will have a different effect on sound.
What affect do the sizes make?
As mentioned, larger boxes have a lower Qtc, which means it will have a flatter response, better low frequency extension, higher efficiency (less mechanical power handling) and better transient response and group delay. Smaller boxes have a higher Qtc, which has a hump in the response (again, in the lower midbass/upper bass area) and more overall output, but less efficiency (higher mechanical power handling), less low frequency extension and worse transient response and group delay than the larger boxes (lower Qtc boxes).
Qtc is a measure of the response and resonance of the "system" (the sub in the box). It "tells" you what box size will have certain affects on the sub and the subs output. For example, a box with a Qtc of .707 will have maximally flat frequency response and the lowest F3 (basically, best low frequency extension) of all the boxes with a transient response and group delay that are "acceptable". A box with a Qtc of .5 has optimal transient response. A box with a Qtc of .577 has maximum group delay. But the .5 and .577 will have a lot less output.
And it's the T/S parameters we use to determine the box size and Qtc that the box size gives us. That's how box programs work. But, it doesn't work in every situation.....take, for example, the 12" RL-p that I have coming to me. When you load it up into a box program (winISD, etc) or into a Qtc calculator....the results are just weird. It's like it specs out as a midbass rather than a sub (for a Qtc of .707, it gave me a box size of .219cuft with an F3 of like 101hz). But, in the real world the sub works just fine in boxes .75 - 1.5cuft