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'Directivity Factor' and 'Directivity Index' - what are they?

The directional characteristics of a sound source are changed substantially by the reflecting surfaces around it. This can be quantified by Directivity Factor and Directivity Index...


The directional characteristics of a sound source are highly influenced by nearby reflecting surfaces.

Take the example of an omnidirectional source - one that radiates sound equally in all directions.

Imagine that this source is placed on a flat, reflecting surface. Its sound output is now constrained within half of the space that it would be if the surface were not present. So all of the energy is constrained within half the space, therefore the sound intensity in that space is twice as great.

This is equivalent to a 3 dB increase in level.

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Suppose now that the same source is placed at the junction of two flat, reflecting surfaces. These could be, for example, a wall and floor of a room.

Now the full output power of the source is constrained within one quarter of the original free space. Therefore within this quarter space, the sound power is increased by four times. The level rises by 6 dB.

Within a room with flat surfaces all at 90 degree angles to each other, the extreme situation is where the floor (or ceiling) and two walls intersect. Now the full power of the source is constrained within one eighth of the original space. So the sound intensity is increased eight times - an increase of 9 dB.

These figures correspond to the Directivity Factor and Directivity Index according to the this table:

Source Location Directivity Factor Directivity Index (dB)
Free field, i.e. suspended between floor and ceiling 1 0
On a flat plane, i.e. on the floor 2 3
At the junction between two perpendicular planes, i.e. floor and wall 4 6
At the junction of three perpendicular planes, i.e. in a corner 8 9

As is common in acoustics, an understanding of these simple principles forms the basis of a feeling for the way in which real sounds interact with real acoustic spaces.

Directivity Factor and Directivity Index can also be applied to sound sources that are in themselves directional, and very similar concepts applied to the directional pattern of a microphone.

By David Mellor Wednesday July 13, 2005

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