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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:

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
L_p = L_w + 10 log(Q/4πr² + 4/R) + 10.3

Where:

L_p = sound pressure level, dB re 20 µPa
L_w = 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 = S_iα_i / ∑_iS_i

where S_i is area of ith surface and α_i is absorption coefficient for ith surface.

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

Equation 4
L_p = L_w + 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:

• 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