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Intensity and distance
Intermediate
Spherical spreading follows the inverse-square law.
I = P/4πr²From a point source I = P/4πr², so doubling the distance gives one quarter of the intensity (6 dB drop).
A 100 W source at 10 m: 0.08 W/m².
Valid in open space without reflections.
In more detail
For a point source, intensity falls with the square of distance, because the power spreads over a sphere. Doubling the distance reduces intensity to one quarter.
Real-world uses
- Loudspeakers are placed to cover an area evenly for listeners.
- Radio signal strength falls with distance in the same way.
- A sound source's loudness falls by a quarter when the distance from it doubles, because the sound spreads over four times the area.
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Frequently asked questions
Does doubling distance halve the sound?
No, it reduces intensity to one quarter, which is about 6 dB quieter.
Does this assume free space?
Yes. Walls and absorption change the pattern in real rooms.
Does sound always fall off this way?
In open air with no reflections, yes. In a room, reflections and absorption change how the level varies with distance.
Related topics in Waves & Sound
Pitch and frequency · Loudness and intensity · Decibel scale · Timbre · Range of hearing · Ultrasound