Subwoofer tools.
THE REFERENCE / 01

Units & assumptions

Every number needs a convention. These are the units, reference conditions, and model boundaries used throughout SubwooferTools.

SI units inside every equation

Calculator fields can accept liters, cubic feet, inches, millimeters, and square centimeters. They are converted before calculation. Changing the unit selector preserves the physical value.

1 L=10−3 m3,1 cm2=10−4 m2,1 mm=10−3 m1\ \mathrm{L}=10^{-3}\ \mathrm{m^3},\quad1\ \mathrm{cm^2}=10^{-4}\ \mathrm{m^2},\quad1\ \mathrm{mm}=10^{-3}\ \mathrm{m}
1 in=0.0254 m,1 ft3=0.028316846592 m31\ \mathrm{in}=0.0254\ \mathrm{m},\qquad1\ \mathrm{ft^3}=0.028316846592\ \mathrm{m^3}

Default air and pressure references

Here c is sound speed, rho is air density, and p_ref is the reference pressure for sound-pressure level. Relevant calculators expose sound speed and density in their air and conventions inputs. A dry-air temperature option uses:

c=343 m/s,ρ=1.20 kg/m3,pref=20 μPac=343\ \mathrm{m/s},\qquad\rho=1.20\ \mathrm{kg/m^3},\qquad p_{\mathrm{ref}}=20\ \mu\mathrm{Pa}

Temperature T is absolute kelvin. Gamma is approximately 1.40, R is approximately 8.3145 J/(mol K), and M is approximately 0.02897 kg/mol. This does not model every effect of humidity. Air density remains an independently specified input.

Optional dry-air temperature model

c=γRTM,T=T∘ ⁣C+273.15c=\sqrt{\frac{\gamma RT}{M}},\qquad T=T_{^\circ\!C}+273.15

Frequency-domain and RMS conventions

Electrical drive voltages, currents, volume velocities, and sound pressures are RMS phasors unless stated otherwise. The peak/RMS conversion shown applies to a sinusoid.

Xmax is one-way peak displacement, not peak-to-peak travel. Manufacturer definitions of Xmax differ; it is not a universal distortion threshold.

ω=2πf,s=jω\omega=2\pi f,\qquad s=j\omega
xpeak=2 xRMSx_{\mathrm{peak}}=\sqrt2\,x_{\mathrm{RMS}}

Net means available chamber air

Net box volume means the air volume available to the enclosure after subtracting the displacement of drivers, braces, internal ports, and other objects. It is not the box's external or unoccupied internal volume.

Internal ducts occupy their enclosed air as well as the duct material. Do not subtract a cabinet wall twice if it also forms part of a slot port.

The compact-source radiation convention

U is radiating volume velocity. A real room or cabinet does not automatically satisfy either idealization. Nearby radiators are added as complex pressures with their propagation paths, not by adding separate decibel levels.

p~(r,f)≈ρsU~Ωre−sr/c\widetilde p(r,f)\approx\frac{\rho s\widetilde U}{\Omega r}e^{-sr/c}
Ω=4π(free space),Ω=2π(ideal rigid half-space)\Omega=4\pi\quad\text{(free space)},\qquad\Omega=2\pi\quad\text{(ideal rigid half-space)}

What these models do not promise

Thiele-Small parameters describe small-signal behavior. At high drive levels, suspension and motor nonlinearities, heating, turbulence, enclosure vibration, room response, and protection limiters can substantially change the result. Predictions are a starting design. Measure the completed enclosure and adjust it.

Put the reference to work.

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