T/S + Maths = Help!!!

[Higo]

Hi boys:
I´m building a 2-W speakers (surround) in a sealed box with these T/S:
Revc= 5.6 ohms
Fo= 53.0815 Hz
Zo= 29.8878 ohms
Sd= 0.0132 m2
BL= 7.7514 TM
no= 0.5374 %
SPL= 89.3211 dB
Qms= 1.8709
Qes= 0.4314
Qts= 0.3506
Vas= 16.0287 lts
Cms= 647.8159 uM/N
Mms= 13.8772 grs
Mmd= 13.0052 grs

I build a sealed box of 8.2 lt. This means a QTC 0.6 and Fb 90 Hz
Am I right with the maths?

The mains (sealed box too) have these T/S:
Revc= 6.3 ohms
Fo= 46.2552 Hz
Zo= 30.9856 ohms
Sd= 0.0216 m2
BL= 8.8430 TM
no= 0.5570 %
SPLo= 89.4767 dB
Qms= 2.2011
Qes= 0.5617
Qts= 0.4475
Vas= 32.6946 lts
Cms= 493.4815 uM/N
Mms= 23.9910 grs
Mmd= 22.1657 grs

I build a sealed box of 42 lt. This means a QTC 0.59 and Fb 61 Hz?
Again: Am I right with the maths?

Any help will be appreciated.
Thanks for your time.
Marcelo

 

[LaMa]

To verify this I think you can use a computersimulation which takes account of changes of Le. Try Unibox it's free (but you have to have MS Excel)

 

[kelticwizard]

The basic formula has been known for a long time-the fifties at least.

As you know, when a speaker is placed in a box less than 3 times as large as it's Vas, there is a rise in resonance and in Q.

Fs = free air resonance "free air" means outside the box.
Qts = total free air Q

Fc = resonance in closed box
Qtc = Q in closed box
Vb = volume of box

a = (Vas¸Vb)

So:

Fc = (a + 1)½ X Fs
Qtc = (a + 1)½ X Qts

 

[kelticwizard]

So for the satellites, the folowing important numbers are given:

Fs= 53.0815 Hz
Qts= 0.3506
Vas= 16.0287 lts

For an 8 liter box, we have:

Qts = [(16/8.2) + 1]½ X 0.35 = 0.6
Fs = [(16/8.2) + 1]½ X 53 = 91 Hz.

You are right with the satellites.

For the main speakers of 42 liters:

Fs= 46.2552 Hz
Qts= 0.4475
Vas= 32.6946 lts

Qts = [(33/42) + 1]½ X 0.45 = 0.6
Fs = [(33/42) + 1]½ X 46 = 61.

You are correct with the main speakers as well. Any inductors you place in series with the speakers will raise the Qtc somewhat.