Sound pressure from a point source falls off with the inverse square law — pressure amplitude p is proportional to 1/r, so level in decibels drops 6 dB every time distance doubles:
SPL(r) = SPL(r0) + 20·log10(r0 / r)
A line array is a vertical stack of N cabinets. Instead of one point source, each element i sits at height y_i and is aimed at a small downward angle (its own "splay"), so the array as a whole can be steered to spread evenly over an audience floor that gets both farther away and lower in elevation angle toward the back. This simulator sums the contributions of all N elements at every point of the audience grid:
Coherent (near-field): p(x) = Σ_i A / r_i · cos(θ_i) · e^(i·k·r_i), k = 2πf / c
Incoherent (power sum): p²(x) = Σ_i (A / r_i · cos θ_i)²
where r_i is the distance from element i to the point, θ_i is the angle between that element's aim direction and the point (a simple cosine directivity roll-off standing in for a real cabinet's polar pattern), f is the test-tone frequency, c ≈ 343 m/s is the speed of sound, and k is the wavenumber. Coherent summation keeps the relative phase of each element, so at some frequencies neighbouring cabinets reinforce each other (constructive interference — louder patches) and at others they cancel (destructive interference — combing, visible as banding in the heat map). Power summation discards phase and only adds acoustic energy, which is what happens once wavelengths are short enough, or sources are far enough apart, that phase relationships become effectively random.
- Elements — more cabinets add SPL (up to +6 dB per doubling for fully coherent coupling at low frequency) but the array also gets taller, changing how it steers.
- Array aim — tilts the whole array down toward the crowd; too little and the back row is under-covered, too much and the front rows get blasted.
- Splay pattern — Uniform gives every cabinet the same angular offset from its neighbour; Progressive widens the angle increment toward the bottom of the array, which is the standard real-world trick to compensate for the audience being both closer and lower near the front.
- Frequency — shorter wavelengths (higher f) make interference lobes narrower and more visible in the coherent heat map; switch to Power sum to see the smooth, comb-free coverage a real system's line-source coupling only approximates at low frequency.
Real-world relevance: this is the same reasoning a system engineer runs in array-prediction software (L-Acoustics Soundvision, d&b ArrayCalc) before hanging a PA rig — getting splay and downtilt right is what keeps level consistent from the barricade to the last row.