# Sound Power and Sound Pressure Levels

## What is Sound Power? How is it related to Sound Pressure?

Sound power is the acoustic energy emitted by a source which is transmitted as sound pressure waves through different media such as air or water. In air, the sound-pressure level (Lp) is related to the sound power level (Lw) by the formula:

Lp = Lw – 10 x Log10 (A)

Where A is the surface area (m2) at the given distance from the source. The area of a hemisphere of radius r metres is given by 2πr2 so the sound pressure level at a distance r from a point source on the ground that emits sound equally in all directions is given by:

Lp = Lw – 10 x Log10 (2πr2) = Lw – 10 x Log10 (2π) – 10 x Log10 (r2)

As 10 x Log10 (r2) = 20 x Log10 (r) and 10 x Log10 (2π) ≈ 8, this can be rewritten as:

Lp = Lw – 20 x Log10 (r) – 8dB

Similarly, if a source is at the bottom of a concrete shaft of cross sectional area A(m2), ignoring any absorptive losses or other attenuating effects, the average sound pressure level some distance up the shaft will be given by:

Lp = Lw – 10 x Log10 (A)

The ISO 374x series of standards make use of this relationship to determine the sound power level of a source from a series of sound pressure level measurements taken over a surface that surrounds the source.