Free-Field Sound Distance

Estimate sound level at a second distance from the same point source in a free field.

How this calculation works

This distance relation estimates the change in sound-pressure level caused by geometric spreading from the same point source. Enter a measured reference level, its distance from the source origin and the target distance from that origin. The logarithm of the distance ratio gives attenuation, which is subtracted from the reference reading. Moving farther away gives positive attenuation and a lower predicted level; moving closer gives negative attenuation and a higher level. Both positions must remain in the source's far field with unchanged directionality and unobstructed propagation. Reflections, barriers, atmospheric absorption and background sound are excluded. The estimate therefore should not be applied directly to reflective rooms, line sources or near-field positions simply because a distance measurement is available.

Inputs and units

Measured reference sound-pressure level (dB)
Reference distance from source (m)
Target distance from source (m)

Method and formula

L2 = L1 − 20 log10(r2/r1), where r1 and r2 are distances from the same point-source origin.

Worked example

Example inputs

Measured reference sound-pressure level: 80 dB
Reference distance from source: 1 m
Target distance from source: 4 m

Calculation steps

Calculate the target-to-reference distance ratio: 4/1 = 4.
Find geometric attenuation: 20 × log10(4) = 12.041200 dB.
Subtract attenuation from the 80 dB reference: Ltarget = 80 − 12.041200 = 67.958800 dB.

Example results

Estimated target sound-pressure level: 67.95880017 dB
Geometric attenuation (negative if closer): 12.04119983 dB

Assumptions

Far-field point source with unchanged directionality and unobstructed geometric spreading

Limitations

Excludes reflections, barriers, atmospheric absorption and background noise
Not applicable to line sources or source near fields

Sources

OSHA Technical Manual: Noise: Free-field sound propagation; approximately 6 dB reduction per distance doubling