Sealed boxes are an exercise in one degree of freedom. Box size determines response shape, which is governed by Qtc. Qtc is a parameter which may usefully vary from 0.5 to 1.5. For High fidelity response, values between 0.5 and 0.7 are recommended. If you prefer a fuller, boosted bass, aim for the high end of the range given. Note: Qtc cannot be less than Qts.
Fb = Fs * sqrt(Vas/Vb+1)
Qtc = Qts * sqrt(Vas/Vb+1)
solving for box size:
Vb = Vas/((Qtc/Qts)^2-1)
or
Vb = Vas/((Fb/Fs)^2-1)
Calculating F3
A1=1/Qtc^2-2
F3 = Fb*sqrt((A1+sqrt(A1^2+4))/2)
For A1>=0, there is no peak in response.
If A1<0, the magnitude of the peak is:
dB=10*log(4/(4-A1^2))
The value of the response at Fb is dB = 20*log(Qtc)
Damped Sealed Boxes (after Small-Margolis, 1981 JAES)
Choose desired Qtc, calculate:
Qtcp=1/(1/Qtc-1/Qa)
L=Qtcp/Qts
alpha = L^2-1
Vb = Vas / (alpha*gamma)
Fb=L*Fs
These equations were developed for fiberglass fill, YMMV for other material. From the article:
For a lined box Qa=10, gamma = 1.0
For a stuffed box Qa=5, gamma = 1.2
Calculate F3 as above. You will find that stuffing materials or other damping methods act somewhat as a notch filter at resonance. Qtc is reduced, but F3 goes up in frequency.
For a more extreme effect, one can make a controlled leak. I found some published designs using variovents and I came up with the following values myself. These are not tested, but seem to give realistic results.
For a variovent or aperiodic enclosure, try Qa=2.5, gamma=1.4 to 1.5