Toolkit

Stand-alone calculators. Each uses the same tested engine functions as the design lab and shows its equation.

SPL vs distance

Lp₂ = Lp₁ − 20·log₁₀(r₂ / r₁)

Lp₁dBr₁mr₂m

−6.02 dB per doubling of distance. The dashed ideal-line curve (−3 dB/dd) is shown only for contrast — real arrays follow it only in their near field.

At 8 m81.9 dB

Change-18.1 dB

Point sourceIdeal line (ref.)

Power → level

ΔL = 10·log₁₀(P₂ / P₁)

P₁WP₂W

Power is an energy quantity → 10·log. 2× power = +3 dB, 10× = +10 dB. Pressure/voltage are field quantities → 20·log (2× pressure = 4× power = +6 dB).

ΔL+10.0 dB

Power ratio× 10.00

Sensitivity calculator

SPL(r) ≈ S + 10·log₁₀(P) − 20·log₁₀(r)

Sensitivity (1 W/1 m)dBPowerWDistancemTargetdB

SPL @ 1 m123.0 dB

SPL @ 20 m97.0 dB

Power for 95 dB @ 20 m252 W

Linear model: real drivers compress several dB near full power. Check whether the sheet quotes sensitivity at 1 W or 2.83 V, and half-space or free field.

Vertical coverage on the floor

d_near = Δz / tan(tilt + V/2), d_far = Δz / tan(tilt − V/2)

Speaker heightmEar heightmTilt (− = down)°Vertical coverage°

Horizontal and vertical scales differ. Shaded band = floor between the nominal −6 dB edges.

Near −6 dB edge6.9 m

Far −6 dB edgebeyond horizon

Aim point17.9 m

Delay calculator

delay(ms) = (d_main − d_delay) / c × 1000 + t_precedence

Main → listenermDelay spk → listenermTemperature°CPrecedencems

Δd17.2 m

c343.2 m/s

Geometric delay50.1 ms

Set delay to60.1 ms

At 343 m/s, 17.2 m ≈ 50.1 ms. The precedence offset (typically 5–15 ms) keeps the image on the main system.

Speed of sound

c ≈ 331 + 0.6·T | c = 331.3·√(1 + T/273.15)

Temperature°C

343 m/s ≈ 20 °C.

Linear343.0 m/s

Ideal gas343.2 m/s

Time for 100 m291.4 ms

Ideal gasLinear

dB addition

L_total = 10·log₁₀( Σ 10^(Lᵢ/10) )

Levels (dB), comma separated

Two equal incoherent sources: +3.0 dB. Coherent and in phase they could reach +6.0 dB at some frequencies — and cancel at others. The platform uses the energetic sum.

Energetic (incoherent) sum93.9 dB

Coherent in-phase bound96.9 dB

Arithmetic (wrong)181.8 dB

10·log₁₀(10^(91.2/10) + 10^(90.6/10)) = 93.9 dB

Inverse-square law

I₂/I₁ = (r₁/r₂)² ⇒ r₂ = r₁ · 10^(ΔL/20)

Reference distancemLevel dropdB

Intensity falls with the square of distance; level in dB falls 20·log₁₀ of the distance ratio.

Distance for −10 dB15.8 m

Distance ratio× 3.16

Intensity ratio1.00e-1

5.0 m	0.0 dB	I × 1.0
10.0 m	-6.0 dB	I × 0.25
20.0 m	-12.0 dB	I × 0.063
40.0 m	-18.1 dB	I × 0.016
80.0 m	-24.1 dB	I × 0.0039
160.0 m	-30.1 dB	I × 0.00098

Ceiling speaker spacing

D = 2·h·tan(θ/2); s = D · {1 | 1/√2 | 1/2}

CeilingmEar heightmCoverage (conical)°Criterion

Room WmRoom Lm

Coverage diameter D4.00 m

Spacing s2.83 m

Grid for 12 × 16 m5 × 6 = 30 speakers

Coverage width

w = 2·d·tan(θ/2)

Coverage angle θ°Distance dm

At the edge of w the level is ~6 dB below on-axis at the same distance (nominal −6 dB definition).

Width at distance24.0 m

Line sources — near vs far field (educational)

ideal line −10·log₁₀(r) · point −20·log₁₀(r) · r_t ≈ H²·f/(2c)

ElementsElement spacingmFrequencyHz

Array height H3.85 m

Transition (coherent, 1000 Hz)≈ 21.6 m

Finite line (incoherent)Point −6 dB/ddIdeal line −3 dB/dd

The finite line (energetic sum of N elements) starts near −3 dB/dd and bends to −6 dB/dd. A real coherent array is frequency dependent and curved: use the manufacturer’s prediction data. This platform never applies −3 dB/dd to a real array.