Inverse Square Law (Sound)
Definition
Inverse Square Law (Sound)
The inverse square law states that sound intensity from a point source decreases proportionally to the square of the distance, resulting in a 6 dB reduction in SPL for each doubling of distance in a free field. This fundamental acoustic principle governs speaker coverage design, SPL prediction at distance, and the balance between direct and reverberant sound in rooms. SonaVyx uses the inverse square law in SPL distance calculations.
SPL₂ = SPL₁ - 20 × log₁₀(d₂/d₁) dB, yielding -6 dB per distance doubling
How It Is Measured
The inverse square law is validated by measuring SPL at multiple distances from a speaker in a free-field environment (outdoors or in an anechoic chamber). SonaVyx can measure SPL at different positions and calculate whether the observed level drop matches the theoretical 6 dB per doubling. In rooms, the direct sound follows the inverse square law while reverberant level remains approximately constant, allowing calculation of the critical distance.
Practical Example
A PA speaker produces 100 dB SPL at 1 meter. Using the inverse square law: at 2 meters the level drops to 94 dB, at 4 meters to 88 dB, at 8 meters to 82 dB, at 16 meters to 76 dB, and at 32 meters to 70 dB. In a reverberant room with a reverberant field of 85 dB, the critical distance (where direct equals reverberant) is approximately 5.6 meters.
Free Field vs Reverberant Field
The inverse square law applies precisely in a free field (outdoors, away from reflective surfaces). In enclosed spaces, the reverberant field creates a constant background level that limits how much SPL decreases with distance. Beyond the critical distance, SPL remains approximately constant regardless of further distance increase. Understanding this transition is essential for PA system design and coverage prediction.
Critical Distance
The critical distance (Dc) is where direct sound level equals the reverberant field level. Beyond this distance, increasing speaker output raises the reverberant level without improving direct-to-reverberant ratio. Critical distance depends on speaker directivity (Q) and room absorption: Dc = 0.057 × √(Q × A), where A is total absorption in Sabins. More directional speakers and more absorptive rooms extend the critical distance, improving intelligibility at greater distances.
Line Arrays
Line arrays deviate from the point-source inverse square law. In the near field, a coherent line array produces cylindrical wave propagation, losing only 3 dB per distance doubling instead of 6 dB. This extended throw capability allows line arrays to cover large audiences with more uniform SPL than point sources. The transition to spherical propagation (6 dB/doubling) occurs at a distance dependent on array length and frequency.
Try It Now
Verify inverse square law — measure SPL at distance with SonaVyx