Enter the sound level and distance at point 1, and the sound level at point 2 into the calculator to find the distance at point 2.
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Decibel Distance Formula
The following formula is used to estimate the distance between two points from the change in sound level (in dB) assuming free-field spherical spreading (no major reflections) and the same reference for both sound level readings.
Dā = Dā Ā· 10^{((Lā ā Lā)/20)}
- Where Dā is the distance at point 2
- Dā is the distance at point 1
- Lā is the sound level at point 2 (dB)
- Lā is the sound level at point 1 (dB)
Because decibels are logarithmic, you canāt take a simple ratio of dB values. Instead, use the relationship between sound level change and distance: a change of 20Ā·logāā(Dā/Dā) dB corresponds to a distance ratio of Dā/Dā.
Decibel Distance Definition
What is decibel distance? āDecibel distanceā commonly refers to the distance at which a sound level (in dB) would be expected to occur, given a known sound level at a different distance, under an assumed spreading model (often free-field spherical spreading).
Example Problem
How to calculate decibel distance?
- First, determine the sound level at point 1.
The sound level at point 1 in this example is found to be 20 dB.
- Next, determine the distance from the source at point 1.
The distance from the sound source to point 1 is found to be 20 ft.
- Next, determine the sound level at point 2.
The sound level at point 2 is found to be 3 dB.
- Finally, calculate the distance to point 2 from the source.
The final distance is calculated to be Dā = 20 Ć 10^((20 ā 3)/20) = 141.59 ft.
About Decibel Distance
How does sound change with distance? In a free field (approximately spherical spreading from a point source), sound intensity follows an inverse-square law (ā 1/rĀ²), and sound pressure level (in dB) decreases by 20Ā·logāā(r) ā about 6 dB for each doubling of distance.
