Let’s consider the sound power flowing through an area. In whole space that area is spherical, and it can be calculated for a known radius using the equation shown.

If the radius is in meters, then the area is in square meters.The one watt of sound power will flow through this spherical area as it propagates outward. Sound power per unit area is sound intensity, and it is in units of watts per square meter. As the distance from the source increases, the surface area of the sphere increases, and the sound intensity drops predictably with distance. So, while sound power is not distance-dependent, sound intensity is.

When radiating energy, it is often desirable to concentrate it in one direction. This increases the intensity in the chosen direction by redirecting energy that would have gone elsewhere.

If the radiation is made hemispherical, the sound power must now pass through one-half the area, so the power-per-unit-area is doubled. This makes the sound intensity level increase by 3 dB when compared to whole space radiation.

The take-away is that constraining the sound power to pass through a smaller unit area has produced a sound intensity increase. We can compensate for the sound intensity drop due to increasing distance from the source by making the source directional. This can allow a given amount of sound power to reach a further listener.