Distance for a Target SPL
The distance at which the sound pressure level falls to a target.
Example
You enter
- SPL at reference (dB) 110
- Reference distance (ft) 1
- Target SPL (dB) 84
- Mode free_field
- Identical sources 1
You get
- Distance for the target level 20.0 ft
Checked against published worked examples from: QSC.
Details, formula, and sources
Scoped2 = d1 x 10^((L1 + mode_factor + 10 log10(N) - L2) / 20). A 110 dB source at 1 ft drops to 84 dB at about 20 ft in free field (every doubling of distance loses 6 dB). Answers 'how far to the hearing-safe or spill line' instead of the level at one spot. Includes the mode adjustment and N incoherent sources; a target above the source level is flagged. A planning estimate; the room and the measurement govern.
Formula or tabled2 = d1 x 10^((L1 + mode_factor + 10 log10(N) - L2) / 20); the inverse of L2 = L1 - 20 log10(d2/d1).
Source and editionClassical acoustics (inverse-square law); ISO 9613-2 (Acoustics - Attenuation of sound during propagation outdoors) by name.
Free accessInverse-square principle free in physics texts; ISO 9613-2 licensed.
What governsEstimate. AHJ and licensed professional govern.
API field namesL1_dB, d1, target_L2_dB, mode, n_sources, d2
- Inverse-square inverse d2 = d1 x 10^((L1 + mode_factor + 10 log10(N) - L2)/20); the target must be below the adjusted reference level or it is rejectedinverse-square law
- Mode adjustments free-field 0 dB / hemispherical +3 dB (half-space) / indoors +6 dB (a rough quarter-space approximation)ISO 9613-2 typical