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### Converting Sound Power to Sound Pressure Formulas and Calculator

**Civil Engineering and Design**

**Design Applications **

**Converting Sound Power to Sound Pressure Formulas and Calculator **

Designers are often required to use sound power level information of a source to predict the sound pressure level at a given location. Sound pressure at a given location in a room from a source of known sound power level depends on:

- room volume,
- room furnishings and surface treatments,
- magnitude of sound source(s),
- distance from sound source(s) to point of observation, and
- directivity of source.

The classic relationship between a single-point source sound power level and room sound pressure level at some frequency is

*Equation 1
L _{p} = L_{w} + 10 log(Q/4πr^{2} + 4/R) + 10.3
*

Where:

*L _{p}* = sound pressure level, dB re 20 µPa

*L*= sound power level, dB re 10

_{w}^{-12}W

Q = directivity of sound source (dimensionless)

r = distance from source, ft

R = room constant, Sα /(1 – α) Equation 2

S = sum of all surface areas, ft^{2}

α = average absorption coefficient of room surfaces at given
frequency, given by:

*Equation 3
α = ∑ _{i} = S_{i}α_{i} / ∑_{i}S_{i}*

where *S _{i}* is area of ith surface and

*α*is absorption coefficient for ith surface.

_{i}If the source is outdoors, far from reflecting surfaces, this relationship simplifies to:

*Equation 4 *

L_{p} = L_{w} + 10 log(Q/4πr^{2}) + 10.3

This relationship does not account for atmospheric absorption,
weather effects, and barriers. Note that r^{2} is present because the
sound pressure in a free field decreases with 1/r^{2} (the inverse-square
law; see the section on Sound Transmission Paths). Each time the
distance from the source is doubled, the sound pressure level
decreases by 6 dB.

Related:

- Acoustic Sound Pressure Level Chart
- Acoustic Definitions and Terms
- Sound System Design Equations
- Speed of Sound Table Chart

References:

- Warnock 1997, 1998a, 1998b)
- AHRI Standard 885