Handbook for Sound Engineers

Computer Aided Sound System Design 1347

natural sound sources show a similar increase giving
rise to a corresponding timbre change.
For approximate calculations or also measurements
of the front to random index, one has to cover at least
the range between 500 and 1000 Hz. Many manufac-
turers are indicating, in the data sheets of their products,
the frequency dependence of directivity.
By means of the front to random index C and the
nominal power rating Pn it is also possible to describe
the characteristic sound level of a loudspeaker system:

(35-13)

where,

LW is the sound power level.

The efficiency of a loudspeaker system is deter-

mined by the ratio between radiated acoustic power and

supplied electric power:

(35-14)

where,

Pak is the acoustic sound power,

Pel is the electrical power applied,

EK is the sensitivity of the loudspeaker,

r 0 is 1 m distance,

Jis the front to random factor of the loudspeaker,

U 0 c is the characteristic acoustic impedance of

air = 408 Pa s/m^3 at 20°C.

By combining all constants one obtains the
following approximation:

. (35-15)

This correlation can be seen in Fig. 35-8. The effi-
ciency of loudspeaker systems lies in reality between
0.1% and 10%. As is the case with the rated sensitivity,
the efficiency is often referred to the nominal imped-
ance Zn of the loudspeaker and designated as nominal
efficiency Kn:

(35-16)

where,
is the direct sound pressure,

Zn is the nominal impedance,

JL is the front to random factor of the loudspeaker.

Eqs. 35-14, 35-15, and 35-16 suggest that because of

the frequency dependence of the front to random index

and the insignificant frequency dependence of the free-

field sensitivity, the loudspeaker system efficiency may

as well depend heavily on the frequency.

Directional Properties. All loudspeakers used in real

life show a more or less pronounced directional depen-

dence of radiation, which is frequency dependent—just

like beaming behaviors. This angular dependence of

sound radiation is characterized by three quantities that

are going to be considered in detail.

The angular directivity ratio * for a frequency or a

frequency band is the ratio between the sound pressure p

radiated at an angle - from the reference axis, and the

sound pressure p 0 generated on the reference axis at

equal distance from the selected acoustic reference point

(this reference point is selected by the loudspeaker

manufacturer and must be published in data sheets;

generally it is the center of gravity of the loudspeaker

box).^10

. (35-17)

In general *(-)d1. If the maximum of directional

characteristics does not occur at -=0°, then *(-) >1.

The logarithmic quantity of the angular directivity

ratio is the angular directivity gain

(35-18)

Fig. 35-9 shows the directional characteristic of the

horn loudspeaker in a polar plot of the directivity gain.

One sees the main maximum at 0° and several

secondary maxima at higher frequencies.

LK LW+= C–11 dB 10 logPn–

K

K

Pak

Pel

--------=

EK

2

U 0 c

---------

4 Sr 0

2

JL

u--------------

©¹

̈ ̧

§·

= u100%

K 3

EK

2

JL

= %---------

Kn

p ̃d

2

Zn

JLu ̃^2

--------------^4 Sr

2

U 0 c

= u-----------

p ̃d

Figure 35-8. Efficiency of a loudspeaker as a function of

rated sensitivity and front to random factor.

*- p

̃ -

p ̃ 0

=-----------

D - = 20 log*- dB