A closed box is not best suited for low frequency reproduction as the roll-off can be as low as 12dB/oct. below the -3dB point (F3, fsb), which means that the sound pressure level drops rapidly below the -3dB point. However actual roll-off is largely determined by the enclosure volume in conjunction with the Q factor of the loudspeaker, the lower the Q factor the lower the roll-off. A closed box has a few advantages though which are quite suitable for our design. For example a woofer with a low Q factor offers a very fast and accurate response in small closed box. Furthermore the air inside the closed box will limit the excursion of the woofer at low frequencies.
Mounting the XLS10 in a 30-liter enclosure means that the total quality factor, that is the Q factor of the woofer and the enclosure combined (Qtc) drops to about 0.3. Normally a value between 0.5 and 0.7 is considered ideal for accurate low frequency reproduction from a closed box. Hence in this case the 30-liter enclosure has a F3 of 78Hz and a very low Q factor which means the frequency response extends far down and the slope of the frequency response is reduced to about -6db/octave below F3 as per the below shown graphs.
In order to determine whether the XLS10 in a 30-liter closed box is able to meet the other requirements, we have to model the box again, but now factoring in the power input to the woofer. The requirement we set is a spl of at least 100dB at 20Hz. The XLS10 can handle up to 300-watts nominal input. But that number is meaningless if we donít also factor in the maximum excursion. As obviously the woofer needs to be kept below its maximum excursion. Plotting the graphs for a power input of 300-watts yields the following results as shown in the graphs below.
As can be seen from the second graph the woofer already reaches maximum excursion at 30Hz, at 20Hz it is increased to 17.4mm, well over the safe limit. Hence it is safe to say that even with a low total Q of 0.3 the XLS10 is unable to produce 100db at 20Hz in a closed box of 30-liter volume. Modeling the box again for 60-liter, double the volume, or 15-liter, half the volume, yields similar results. Obviously the next thing to try is a vented box, of similar volume, to see whether that yields better results.