Stand next to a loudspeaker and walk away. The sound gets quieter, and quickly at first. The reason is that the sound energy spreads out.

Imagine a tiny source in the open air, sending the same power in every direction. At distance r the energy is spread over a sphere of area 4πr². Double the distance and the sphere has four times the area, so each square metre gets a quarter of the intensity. This is the inverse square law: I ∝ 1/r².

In decibels, the change between distance r₁ and r₂ is ΔL = −20 × log₁₀(r₂ / r₁). In practice:

• Doubling the distance lowers the level by 6 dB.
• Ten times the distance lowers it by 20 dB.

Example: a source of 90 dB at 1 m. At 2 m it is 84 dB, at 4 m 78 dB and at 8 m 72 dB (the formula gives 71.9 dB, which we round).