# Sound - Abatement vs. the Distance from Source

The sound pressure from a source is reduced with distance from source.

### Spherical Distance

Sound pressure in spherical distance from a noise source can be calculated as:

p^{2}= ρ c N / (4 π r^{2}) (1)

where

p = sound pressure (Pa, N/m^{2})

ρ = density of air (kg/m^{3})

c = speed of sound (m/s)

N = sound power (W)

π = 3.14

r = distance from source (m)

### Half Spherical Distance

Sound pressure in half spherical distance from a source can be expressed as:

p^{2}= ρ c N / (4 π r^{2}/ 2)

= 2 ρ c N / (4 π r^{2}) (2)

A more generic expression for sound pressure in distance from source can be formulated to:

p^{2}=Dρ c N / (4 π r^{2}) (3)

where

D = directivity coefficient (1 spherical, 2 half spherical)

The *directivity coefficient* depends on several parameters - the position and direction of the source, the room and the surrounding area, etc.

The Sound Pressure Level - *L _{p}-* can be expressed logarithmic in decibels as:

L_{p}= 20 log (p / p_{ref})

=20 log ((Dρ c N / (4 π r^{2}))^{1/2}/ p_{ref})

= 20 log (1 / r (Dρ c N / (4 π))^{1/2}/ p_{ref}) (4)

where

L_{p}= sound pressure level (dB)

p_{ref}= 2 10^{-5}- reference sound pressure (Pa)

**Note!** - a doubling of the distance from a sound source - will reduce the sound pressure level - *L*_{p} - with *6 decibels*.

### Sound Pressure Level Calculator

### Example - Sound Pressure from a Wood Planer

The sound power generated from a wood planer is estimated to *0.01 W. *The sound pressure in distance *10 m* from the planner can be calculated as

*L _{p} = 20 log ((Dρ c N / (4 π r^{2}))^{1/2} / p_{ref} )*

* = 20 log (2 (1 kg/m ^{3}) (331.2 m/s) (0.01 W) / (4 π (10 m)^{2}))^{1/2} / (2 10^{-5} Pa))*

* = 71 dB *

## Related Topics

### • Acoustics

Room acoustics and acoustic properties. decibel A, B and C calculations. Noise Rating (NR) curves. Sound transmission through walls. Calculate sound pressure, sound intensity and sound attenuation.

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