Directivity Index

The directivity index DI is just a logarithmic version of the directivity factor Q. It is expressed in decibels.

A directivity index DI_θ,ϕ may be defined, where

(3.59)

(3.60)

Note if the source power remains the same when it is put on a hard rigid infinite surface Q(θ, ϕ) = 2 and DI(θ, ϕ) = 3 dB.

EXAMPLE 3.11

1. If a constant‐volume velocity source of sound power level 120 dB (which is equivalent to 1 acoustic watt) radiates to whole space and it has a directivity factor of 12 at 50 m, what is the sound pressure level in that direction?
2. If this constant‐volume velocity source is put very near a hard reflecting floor, what will its sound pressure level be in the same direction?

SOLUTION

1. We have that I = 1/4π(50)² = 1/10⁴ π (W/m²), thenBut for the directional source L_p(θ, ϕ) = 〈L_p〉_S + DI(θ, ϕ), then assuming ρ c = 400 rayls, L_p(θ, ϕ) = 75 + 10 log 12 = 75 + 10 + 10 log 1.2 = 85.8 dB.
2. If the direction is away from the floor, then