Relationships between Qtc, F3, Fb in acoustic suspension enclosure

[presscot]

Let’s focus on a sealed enclosure system, there are engineering terms involving Qtc, F3, and Fb.

Firstly, I’m not sure whether I can call ‘Fb’ as “the tuning frequency of the box” because I used to be told that the closed box has NO tuning frequency. He suggested me to call it as the “box resonance” instead of the previous word. So, I’d like to hear opinions whether his statement is true. Can I call ‘Fb’ as the tuning frequency (of the closed box)?

Secondly, if we consider Qtc of a conventional system, it would be recognized as Qtc of 0.707. And it will give F3 at the same frequency as Fb (F3 = Fb). To my understanding if Qtc is lowered than 0.707, the result will become F3 > Fb, and vice versa for the opposite case (Qtc > 0.707 ==> F3 < Fb). Does my understanding correct?

Finally, assume we have a closed box system that is specified as F3 = 28Hz and Fb = 36Hz. It’s clearly seen that this system will be categorized as Qtc > 0.707 (underdamped). But, if the F3 occurs at approximately 50Hz, it becomes an over-damped instead (Qtc < 0.707). So, does it mean the underdamped characteristic will be better choice since it produces lower F3. IOW, it provides deeper bass output. Is my assumption correct? However, this assumption is based on the fixed Fb (@ 36Hz). I’m not sure if it will be available in the real world. And if it doesn’t appear, how does the Fb behave regarding the F3?

 

[AllenB]

A closed box is a compliance which appears in series with the driver compliance so that they work as one. The result is second order, just as the driver on it's own.

 

[cabirio]

https://sdlabo.jp/archives/Closed_Box_Loudspeaker_Systems_Part_1-2.pdf

See in particular "3 - Response".

 

[AllenB]

presscot, the above paper is good but there is more to Figure 4 than meets the eye. As it stands this shows responses over a range of damping but to compare them for a given box, you need to slide the frequencies according to the scale of the X axis.

 

[planet10]

Let’s focus on a sealed enclosure system, there are engineering terms involving Qtc, F3, and Fb

Q_tc, F₃, and V_as determine F_b (and box Q).

dave

 

[cabirio]

presscot, the above paper is good but there is more to Figure 4 than meets the eye. As it stands this shows responses over a range of damping but to compare them for a given box, you need to slide the frequencies according to the scale of the X axis.

Good point. This is the set of plots for a given driver (I chose randomly a Scan Speak 26W/8534G00) in different sized boxes to give those Q values. I think this illustrates better what happens when you adjust your box size to achieve different FRs:

These are the Vb, F3 and Fb values in each case:

Q = 0.5 -> Vb = 167.7 l, F3 = 47.9 Hz, Fb = 30.9 Hz
Q = 0.71 -> Vb = 47.2 l, F3 = 45.1 Hz, Fb = 45.1 Hz
Q = 1.0 -> Vb = 18.0 l, F3 = 52.5 Hz, Fb = 66.8 Hz
Q = 1.4 -> Vb = 7.3 l, F3 = 71.8 Hz, Fb = 101.5 Hz
Q = 2.0 -> Vb = 2.8 l, F3 = 108.1 Hz, Fb = 160.4 Hz

Edit: just to add that looking solely at F3 as the parameter that determines how low your speaker will go is misleading. Compare above the 0.5 and 0.71 responses: although F3 for the first one is higher, you can clearly see that, below that point, the roll-off is more gentle and e.g. at 20 Hz you clearly will have more output from it than from the one with the lowest F3.

 

[DualTriode]

Hello All,

One rule of thumb I have observed is that F3 is very near the Resonant Frequency of the driver in the sealed box and QTb is at or near 0.71 + /- a fairly wide range in QTb.

Thanks DT