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

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:

1. room volume,
2. room furnishings and surface treatments,
3. magnitude of sound source(s),
4. distance from sound source(s) to point of observation, and
5. 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
Lp = Lw + 10 log(Q/4πr2 + 4/R) + 10.3

Where:

Lp = sound pressure level, dB re 20 µPa
Lw = sound power level, dB re 10-12 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, ft2
α = average absorption coefficient of room surfaces at given frequency, given by:

Equation 3
α = ∑i = Siαi / ∑iSi

where Si is area of ith surface and αi is absorption coefficient for ith surface.

If the source is outdoors, far from reflecting surfaces, this relationship simplifies to:

Equation 4
Lp = Lw + 10 log(Q/4πr2) + 10.3

This relationship does not account for atmospheric absorption, weather effects, and barriers. Note that r2 is present because the sound pressure in a free field decreases with 1/r2 (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:

References:

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