Reference: the physics behind every number
The platform is not a black box. These are all the models the simulation uses, with worked examples computed by the same code, and the assumptions that limit them.
Free-field propagation (point source)
| Lp₁ | level at reference distance r₁ (dB SPL) |
| r₂ | distance of interest (m) |
Why?
Sound energy from a small source spreads over a sphere whose area grows with r². Intensity ∝ 1/r², pressure ∝ 1/r, so level falls 20·log₁₀ of the distance ratio: −6.02 dB every time the distance doubles.
Example
Assumptions & limits
- Far field of the source (r ≫ box size)
- No reflections (outdoor free field, or direct sound only indoors)
- No air absorption
Electrical power and level
| P₁, P₂ | electrical power (W) |
Why?
Power is an energy-like quantity, so it uses 10·log₁₀. Pressure, voltage and distance ratios are field quantities and use 20·log₁₀ (because power ∝ pressure²: 10·log₁₀(p²) = 20·log₁₀(p)). Doubling power is only +3 dB; doubling distance is −6 dB.
Example
Assumptions & limits
- Linear loudspeaker (no power compression)
- Same impedance
SPL from sensitivity
| S | sensitivity, dB SPL @ 1 W / 1 m |
| P | input power (W) |
| r | distance (m) |
Why?
Sensitivity gives the level for 1 W at 1 m. Add the power gain (10·log₁₀) and subtract the distance loss (20·log₁₀).
Example
Assumptions & limits
- Simplified model — not a measurement
- Real drivers compress several dB near rated power
- Sensitivity may be half-space or 2.83 V: check the datasheet conditions
Combining sources (energetic sum)
| Lᵢ | level from each source at the listener (dB) |
Why?
Decibels are logarithmic and cannot be added arithmetically. Converting to energy, adding and converting back gives the average level of uncorrelated (incoherent) sources.
Example
Assumptions & limits
- Does NOT model phase, interference, comb filtering or coherence
- Two coherent in-phase sources could reach +6 dB at some frequencies and cancel at others
- The map is a spatial average estimate, not a frequency-resolved prediction
Nominal directivity model (estimate)
| γ | angle between the aim axis and the listener |
| ψ | direction around the axis (0 = horizontal plane) |
| H, V | nominal coverage angles (−6 dB points) |
| floor | lowest attenuation used off-axis / behind (default −20 dB) |
Why?
A datasheet “90° × 60°” means the level is 6 dB below on-axis at ±45° horizontally and ±30° vertically. With only those numbers we interpolate a smooth elliptical pattern. When the manufacturer publishes beamwidth per frequency, those values replace H and V.
Example
Assumptions & limits
- NOMINAL COVERAGE — not measured polar data
- Real patterns change with frequency and have lobes
- Front-to-back ratio unknown: floor is an assumption
Coverage width
| θ | coverage angle (deg) |
| d | distance along the axis (m) |
Why?
Simple trigonometry of the −6 dB coverage triangle. At the edge of that width the level is ~6 dB below the on-axis level at the same distance.
Example
Assumptions & limits
- Measured perpendicular to the aim axis
- Nominal angle, broadband
Speed of sound vs temperature
| T | air temperature (°C) |
Why?
Sound travels faster in warmer air. 343 m/s corresponds to about 20 °C. The simulation uses the ideal-gas expression; the linear one is an easy approximation.
Example
Assumptions & limits
- Dry air; humidity adds < 0.5 %
Delay speakers
| Δd | path difference main → listener minus delay → listener (m) |
| c | speed of sound (m/s) |
Why?
A delay speaker is closer to the listener than the main system. Without delay its sound would arrive first and the image would pull toward it; with too little delay you hear echoes. Delaying it by the travel-time difference (plus ~5–15 ms) lets the main system arrive first (precedence / Haas effect) while the delay adds level.
Example
Assumptions & limits
- Only exact at the reference listening position
- Temperature changes c and therefore the ideal delay
Line sources: cylindrical vs spherical spreading
| H | array height (m) |
| f | frequency (Hz) |
Why?
An infinitely long coherent line radiates a cylinder: −3 dB per doubling of distance. A real array is finite, so it behaves like a line only close to it (near field) and like a point source (−6 dB/dd) beyond the transition distance, which grows with frequency and with the square of the array height.
Example
Assumptions & limits
- Order-of-magnitude estimate for a straight, uniformly driven array
- Curved / shaded real arrays must be predicted with the manufacturer’s data
- This platform does not apply −3 dB/dd to real arrays
Obstacles: barrier diffraction (Maekawa)
| δ | extra path length over/around the obstacle edge (m) |
| λ | wavelength c/f (m) |
Why?
Sound bends around obstacles. The shadow is deeper when the detour is long compared with the wavelength: high frequencies are strongly shadowed, low frequencies much less. The map uses the selected band (1 kHz by default).
Example
Assumptions & limits
- Empirical fit for a thin screen
- Single-edge path; reflections ignored
- Capped at 24 dB
Air absorption (ISO 9613-1)
| α | attenuation coefficient (dB/m), ISO 9613-1 |
Why?
Air converts sound energy to heat, mostly at high frequency. Negligible in a classroom, several dB at 4–8 kHz across a festival field.
Example
Assumptions & limits
- Pure-tone coefficient at band centre
- Applied only when a band is selected
Distributed (ceiling) speaker spacing
| h | ceiling height − ear height (m) |
| θ | coverage angle (deg) |
Why?
Each ceiling speaker covers a circle at ear height. Closer spacing trades more units for more uniform level (±1–2 dB instead of ±6 dB).
Example
Assumptions & limits
- Square grid
- Nominal conical coverage
What this platform is — and isn’t
Predictions are simplified estimates (direct sound, energetic summation, nominal directivity). They do not replace the manufacturer’s own prediction software, room-acoustic modelling or on-site measurement. Manufacturers provide their own prediction tools for their systems, and room-acoustic software models reflections and reverberation. Use this lab to explore options, understand trade-offs and communicate a concept; verify the final design with the manufacturer’s data and on-site measurement.
Precision
Levels are shown with one decimal at most (none in summaries), distances with one decimal. Inputs like datasheet max SPL are typically ±1–3 dB between measurement methods; more digits would be false precision.