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# Directivity Index and Directivity Factor

The gain produced by concentrating the sound energy is called the directivity index - DI. It is expressed in relative dB. A spherical source has a DI = 0 dB. It serves as a reference. Confining the radiation increases the DI beyond this reference condition for listeners within the pattern. The DI can also be expressed as a directivity factor, Q, if converted to linear units. Q is related to inverse area, and can be considered to be the denominator of a fraction that describes the portion of a sphere that the sound energy is confined to.

Q = 1 is 1/1 sphere

Q = 2 is 1/2 sphere

Q = 4 is 1/4 sphere

Q = 8 is 1/8 sphere

And so on. Anyway, I think you get the idea. Confining the sound energy to where we need it, is the key to effective sound reinforcement. If you are a sound system designer, Q is your friend.

Q’s as high as 50 can be achieved at high frequencies with large pattern control horns. It is important to note that both DI and Q are frequency-dependent, and must be plotted vs. frequency to be meaningful. The graph shown gives both on the same plot.

The radiation pattern control may be accomplished by using room boundaries in the low frequency decade, or by horn-loading in the mid and high frequency decades. The required size of the horn is approximately one wavelength in diameter at the frequency of interest. This allows high frequency horns to be physically small and requires that low frequency horns be physically large. A key design parameter is deciding how low in frequency the pattern control can be extended to, given the allowable size of the horn. The largest practical size for a
given application may be determined by the available space, and/or aesthetics.

Line arrays achieve vertical pattern control by using the phase interaction between multiple low directivity transducers. The required array length is inversely proportional to frequency. Low frequency line arrays must be very long.