Computer Aided Sound System Design 1349ation component caused by the loudspeaker in the
excited room.
The square of this quantity is the well-known direc-
tivity factor Q:(35-20)Especially in the United States, it is common to use
just Q for different angles -. Nevertheless this entity is
angle-dependent and therefore it should always be refer-
enced along with the corresponding angle. The loga-
rithmic expression of the directivity factor Q(-) is the
so-called directivity index DI (also angle dependent)(35-21)where,
H(- is the reverberation directional index.In the German literature one uses for the directivity
factor Q, the reverberation directional value g(-).^10 By
the same token the directivity index, DI, is called rever-
beration directional index H(-).
The reader should be aware of the partially contra-
dicting conventions, of which some are using Q and DI
only for values of -= 0° and others employ Q and DI in
an angle-dependent way, sometimes without clearly
stating so.
Transmission Range. According to several standards,
the transmission range of a loudspeaker is the frequency
range usable or preferably used for sound transmission.
That region of the transmission curve in which the level
measured on the reference axis in the free field does not
drop below a reference level generally characterizes the
transmission range. The reference value is the average
over the bandwidth of 1 octave in the region of highest
sensitivity (or in a wider region as specified by the
manufacturer). In the ascertainment of the upper and
lower limits of the transmission range, there are not
considered any peaks and dips whose interval is shorter
than^1 / 8 octave.
This definition implies that loudspeakers have to
necessarily be checked as to their transmission range
before being used in sound reinforcement systems. With
radiators intended for indoor use, it is also necessary to
consider the front to random factor—i.e., the influence
of the diffuse-field component on the formation of the
resulting sound pressure.For special loudspeaker systems—e.g., studio moni-
toring equipment—narrower tolerance fields of the free-
field sound pressure are indicated for the transmission
range. Thus the OIRT Recommendation 55/1 permits
for the range from 100 Hz–8 kHz a maximum deviation
of r4 dB from the average value, whereas below, down
to 50 Hz, and above, up to 16 kHz, the tolerance field
widens to 8 dB and +4 dB.^11
Fig. 35-11 shows exemplary the behavior of free-
field sensitivity, diffuse-field sensitivity, and front to
random index of a radiator.
Moreover the transmission range is influenced, espe-
cially in the lower-frequency range, by the installation
conditions or the arrangement of the radiator. Fig. 35-12
shows that the arrangement of the loudspeaker system
has a considerable influence on the transmission curve.
This is due to the fact that arranging the radiator in front
of, below, or above a reflecting surface causes interfer-
ences of the direct sound by the strong reflections that
give rise to comb-filter-like cancellations, which can be
proven by a narrow-band analysis of the resulting
signal. These cancellations are particularly pronounced,
if the source is in front of a wall, and the radiator has
compensating openings in its rear part, or if these reflec-
tions come from a distance of about 1.5 m out of a room
corner—e.g., between ceiling and wall.As a rule one can say that the ear normally does not
perceive dips and peaks that are not measurable in a
octave band filter analysis (unless they show
pronounced periodic structures).
A good bass radiation is produced if the radiating
plane is embedded in a reflecting surface, for instance, a
wall or a ceiling. In this case there may also exist a
certain angle between the radiating plane and the
surrounding surface.Qg= -=J*^2 -DI=H -
= 10 logg - dB
= 10 logQ - dBFigure 35-11. Frequency dependence of the front to
random index, as compared with the free-field and the
diffuse-field sensitivities.(^1) » 3