2.1 __Point Source__

__
__Let us consider a point source of
acoustic power W watts, suspended in mid-air and radiates sound waves uniformly in all
directions. The sound will spread out spherically and the intensity at any location will
depend on the surface area of the sphere at that location (see Figure l). The sound
intensity, I, in Watt/m2, at any distance r meters from
the source is given by:

(1)

or,

(2)

The above two are alternative
expressions of the **Inverse Square Law** which state that the sound intensity
(outward) is inversely proportional to the square of the distance from the point source.

Recalling the definition of decibels,
we have,

and

Let us compare the sound
intensity and pressure levels at two distances, r1 and r2 from the sound source. We have,

** **(3)

If r2
= 2 r1, then

(4)

In the case of industrial noise
sources, the same general characteristics apply except that usually the problem is much
more complicated, owing to the multiplicity of noise sources within a single machine as
well as the proximity of other noisy machinery. Nonetheless, it is absolutely necessary to
estimate at least the directional characteristics of the noise source in question. This
requirement is met by an estimation of the directivity factor, Q, directly or by an
approximate calculation using the directivity index, DI.

Figure 2 Sound-Pressure-Level Polar Plot of the Radiation Pattern
of a Loudspeaker

The directivity factor,
Q, is defined as the ratio of the intensity (W/m2) at
some distance and angle from the source to the intensity at the same distance, if the
total power from the source were radiated uniformly in all directions.

(5)

where Iq = Sound intensity at distance
r and angle q from the source

I = Average sound intensity over a
spherical surface at the distance r

And the directivity index (DI) is
defined as :

(6)

To take account of any directional effect of the sound source, a
directivity factor Q is defined such that the sound intensity will be given by:

(7)

Using equation (7) it can be proved that :

(8)

where,

Lp = sound pressure level, dB

Lw = sound power level of source, dB

r = distance from the source

Q = directivity factor

The values of Q for some ideal geometry and assuming perfect reflection
are given in the Table 1.